Quiz-summary
0 of 30 questions completed
Questions:
- 1
- 2
- 3
- 4
- 5
- 6
- 7
- 8
- 9
- 10
- 11
- 12
- 13
- 14
- 15
- 16
- 17
- 18
- 19
- 20
- 21
- 22
- 23
- 24
- 25
- 26
- 27
- 28
- 29
- 30
Information
CMFAS CGI Premium Access
You have already completed the quiz before. Hence you can not start it again.
Quiz is loading...
You must sign in or sign up to start the quiz.
You have to finish following quiz, to start this quiz:
Results
0 of 30 questions answered correctly
Your time:
Time has elapsed
Categories
- Not categorized 0%
- 1
- 2
- 3
- 4
- 5
- 6
- 7
- 8
- 9
- 10
- 11
- 12
- 13
- 14
- 15
- 16
- 17
- 18
- 19
- 20
- 21
- 22
- 23
- 24
- 25
- 26
- 27
- 28
- 29
- 30
- Answered
- Review
-
Question 1 of 30
1. Question
Which of the following can be calculated by the specific commands that a basic version of R provides?
Correct
The basic version of R can only provide specific commands for certain functions which include the calculation of the probability mass function, distribution function, and quantiles for binomial, geometric, negative binomial, and Poisson distributions, along with commands for simulation observations.
Incorrect
The basic version of R can only provide specific commands for certain functions which include the calculation of the probability mass function, distribution function, and quantiles for binomial, geometric, negative binomial, and Poisson distributions, along with commands for simulation observations.
-
Question 2 of 30
2. Question
which of the following is true reagading a probability integral transform?
Correct
Probability integral transform is also known as “Universality of Uniform” as it uses a standard uniform distribution of converting the random variables from any given continuous distribution. There are times that the result would be modified or extended so that the transformation would result in the standard distribution.
Incorrect
Probability integral transform is also known as “Universality of Uniform” as it uses a standard uniform distribution of converting the random variables from any given continuous distribution. There are times that the result would be modified or extended so that the transformation would result in the standard distribution.
-
Question 3 of 30
3. Question
What will be the outcome if the conditional expectation formula is added to the conditional variance formula?
Correct
The formula of a conditional expectation is E [E [X │ W]]= E [X] while the formula of conditional variance is Var [X]=E [Var [X │ W]] + Var [E [X │ W]]. When adding the terms of the conditional expectation formula, it will be easy to detect that the right-hand side of the conditional variance formula is equal to the left-hand side.
Incorrect
The formula of a conditional expectation is E [E [X │ W]]= E [X] while the formula of conditional variance is Var [X]=E [Var [X │ W]] + Var [E [X │ W]]. When adding the terms of the conditional expectation formula, it will be easy to detect that the right-hand side of the conditional variance formula is equal to the left-hand side.
-
Question 4 of 30
4. Question
Which of the following are correct about the cumulative distribution function?
I. It can only be defined by continuous and discrete random variables.
II. It is a method that can be defined for any kind of random variable such as discrete, continuous, and mixed.
III. It is a method used to describe the distribution of random variables.
IV. It cannot be defined for the continuous random variable.Correct
The cumulative distribution function of a random variable is as used as one of the methods in describing the distribution of the random variables. the advantage of a cumulative distribution function is that it can be defined for any kind of random variable such as discrete, continuous, and mixed, unlike the probability mass function which can only be used to describe the distribution of a discrete random variable.
Incorrect
The cumulative distribution function of a random variable is as used as one of the methods in describing the distribution of the random variables. the advantage of a cumulative distribution function is that it can be defined for any kind of random variable such as discrete, continuous, and mixed, unlike the probability mass function which can only be used to describe the distribution of a discrete random variable.
-
Question 5 of 30
5. Question
What is the fucntion of simulation in risk modeling?
Correct
Simulation is the gathering of data using a model random events that would stimulate outcomes that would match a realistic outcome with the use of actual objects such as coins and cards. By using simulations in probability, the researcher would gain insight into the real world.
Incorrect
Simulation is the gathering of data using a model random events that would stimulate outcomes that would match a realistic outcome with the use of actual objects such as coins and cards. By using simulations in probability, the researcher would gain insight into the real world.
-
Question 6 of 30
6. Question
What does the function Fx that is characterized as non- decreasing and right-continuous in the formula of cumulative distribution function satisfies?
Correct
The distribution function called cumulative distribution function is given by the formula of Fx(x)=Pr[X≤x],x∈R which satisfies the criteria of 0≤F_X (x)≤1 for all x in R lim┬(n→→∞)〖F_X 〗 (x)=1 and lim┬(n→→∞)〖F_X 〗 (x)=0 which. It satisfies for all in R and which implies that most of the random variables in the distribution is non-negative or would not be less than 0.
Incorrect
The distribution function called cumulative distribution function is given by the formula of Fx(x)=Pr[X≤x],x∈R which satisfies the criteria of 0≤F_X (x)≤1 for all x in R lim┬(n→→∞)〖F_X 〗 (x)=1 and lim┬(n→→∞)〖F_X 〗 (x)=0 which. It satisfies for all in R and which implies that most of the random variables in the distribution is non-negative or would not be less than 0.
-
Question 7 of 30
7. Question
Which of the following is correct about conditioning?
Correct
Conditioning is one of the main tools used in risk modeling. It is often the key to a neat approach to the derivation of properties and features that were considered in risk modeling. The outcome would lead to a non-random result if there is a complete specification of the condition but if the condition is random, the outcome would also be random.
Incorrect
Conditioning is one of the main tools used in risk modeling. It is often the key to a neat approach to the derivation of properties and features that were considered in risk modeling. The outcome would lead to a non-random result if there is a complete specification of the condition but if the condition is random, the outcome would also be random.
-
Question 8 of 30
8. Question
Which of the following statements are correct?
Statement 1: The notation is commonly used for the expected value of a random variable X.
Statement 2: Cumulative distribution function is also known as a continuous functionCorrect
Both statements are wrong because, in the first statement, the notation Fx should be described as a non-decreasing and right continuous function. The notation that is commonly used for the expected value of a random variable x is the notation Ex. The second statement is also wrong as it should be a probability density function instead of a cumulative distribution function as it is the one known as a continuous function.
Incorrect
Both statements are wrong because, in the first statement, the notation Fx should be described as a non-decreasing and right continuous function. The notation that is commonly used for the expected value of a random variable x is the notation Ex. The second statement is also wrong as it should be a probability density function instead of a cumulative distribution function as it is the one known as a continuous function.
-
Question 9 of 30
9. Question
What is the use of standard deviation in probability?
Correct
The Standard deviation of a random variable is measured to know how close the random variable is from the mean. It is called the standard deviation as it represents the “average” (standard) distance (deviation) from the mean.
Incorrect
The Standard deviation of a random variable is measured to know how close the random variable is from the mean. It is called the standard deviation as it represents the “average” (standard) distance (deviation) from the mean.
-
Question 10 of 30
10. Question
What concept of integration came from the combination of ideas of two mathematicians that resulted in a flexible and powerful concept of integration?
Correct
Lebesgue-Stieltjes Integral generalizes the idea of Henri Leon Lebesgue and Thomas Joannes Stieltjes that preserves many advantages in creating a more general measure-theoretic framework. It is associated with any function of bounded variation in the real line.
Incorrect
Lebesgue-Stieltjes Integral generalizes the idea of Henri Leon Lebesgue and Thomas Joannes Stieltjes that preserves many advantages in creating a more general measure-theoretic framework. It is associated with any function of bounded variation in the real line.
-
Question 11 of 30
11. Question
What is the best reason why the use of the statistical software package R is significant in risk modeling?
Correct
Statistical software package R is a system used in carrying out the simulations, statistical analyses, and numerical approximations of random variables. It has a variety of packages that are available wherein users can find a diversity of codes, functions, and features that are designed to be equipped with a large amount of programming and analytical tasks. It is used with the assumption that the user is familiar with how R works and with its basic commands.
Incorrect
Statistical software package R is a system used in carrying out the simulations, statistical analyses, and numerical approximations of random variables. It has a variety of packages that are available wherein users can find a diversity of codes, functions, and features that are designed to be equipped with a large amount of programming and analytical tasks. It is used with the assumption that the user is familiar with how R works and with its basic commands.
-
Question 12 of 30
12. Question
Which of the following is true regarding a probability generating function?
Correct
Probability generating functions are tools useful for dealing with sums and limits of discrete random variables and for some stochastic processes, it also has a special role in analyzing whether a process will reach a particular state. It is often employed for their succinct description of the sequence of probabilities of a random variable and the availability of a well-developed theory of power series with non-negative coefficients.
Incorrect
Probability generating functions are tools useful for dealing with sums and limits of discrete random variables and for some stochastic processes, it also has a special role in analyzing whether a process will reach a particular state. It is often employed for their succinct description of the sequence of probabilities of a random variable and the availability of a well-developed theory of power series with non-negative coefficients.
-
Question 13 of 30
13. Question
What is described as the average of the fourth power of the standard deviations from the mean?
Correct
Kurtosis is the extent to which the peak of a probability distribution deviates from the shape of a normal distribution. The coefficient of kurtosis is the average of the fourth power, the standardized deviation from the mean. In a normal population, the coefficient of kurtosis is expected to equal to 3 wherein a value greater than 3 indicates a leptokurtic distribution while a value less than 3 indicates a platykurtic distribution.
Incorrect
Kurtosis is the extent to which the peak of a probability distribution deviates from the shape of a normal distribution. The coefficient of kurtosis is the average of the fourth power, the standardized deviation from the mean. In a normal population, the coefficient of kurtosis is expected to equal to 3 wherein a value greater than 3 indicates a leptokurtic distribution while a value less than 3 indicates a platykurtic distribution.
-
Question 14 of 30
14. Question
What is it called if the rth central moment lacks symmetry in a frequency contribution?
Correct
The rth central moment of a random variable X is denoted as E[(X-E[X]^r]. The third part in the central moment is called the coefficient of skewness wherein skewness is the term that describes a lack of symmetry in a frequency contribution.
Incorrect
The rth central moment of a random variable X is denoted as E[(X-E[X]^r]. The third part in the central moment is called the coefficient of skewness wherein skewness is the term that describes a lack of symmetry in a frequency contribution.
-
Question 15 of 30
15. Question
What is the distinction of the empirical distribution function from cumulative distribution function?
Correct
The empirical distribution function is a part of the cumulative distribution function which acts as an estimate that generates points in the sample. According to the Givenko-Cantelli theorem, it converges with probability to that underlying distribution. A series of results are used to quantify the rate of the convergence of the empirical distribution function to the underlying cumulative distribution function.
Incorrect
The empirical distribution function is a part of the cumulative distribution function which acts as an estimate that generates points in the sample. According to the Givenko-Cantelli theorem, it converges with probability to that underlying distribution. A series of results are used to quantify the rate of the convergence of the empirical distribution function to the underlying cumulative distribution function.
-
Question 16 of 30
16. Question
What does correlation mean in probability?
Correct
Correlation is a measurement of the strength of the linear relationship between the random variables. In correlation, there would be a positive and negative correlation. A positive correlation is a relationship wherein two variables are leading in the same direction while the negative correlation is a relationship where one of the variables decreases and the other one increases or vice versa.
Incorrect
Correlation is a measurement of the strength of the linear relationship between the random variables. In correlation, there would be a positive and negative correlation. A positive correlation is a relationship wherein two variables are leading in the same direction while the negative correlation is a relationship where one of the variables decreases and the other one increases or vice versa.
-
Question 17 of 30
17. Question
Under the probability theory, which of the following functions are being used to get the probability of a random variable?
I. Probability density function
II. Probability variance function
III. Cumulative distribution function
IV. Probability mass functionCorrect
Probability density function, Cumulative distribution function, and Probability Mass function are functions that can all be used in getting the probability of the likelihood of occurrence of a random variable. The probability variance function is non-existing so it cannot be used in probability theory.
Incorrect
Probability density function, Cumulative distribution function, and Probability Mass function are functions that can all be used in getting the probability of the likelihood of occurrence of a random variable. The probability variance function is non-existing so it cannot be used in probability theory.
-
Question 18 of 30
18. Question
According to the law of Total Variance, what can be concluded if all of the terms in an equation are positive?
I. This states that when we condition on Y, the variance of x reduces on average.
II. This states that when we condition on X, the variance would decompose into two different parts.
III. This proves that there are only a few ways that we can look at the law of total variance to get some intuition.
IV. This proves that the law of total variance can be explained intuitively.Correct
The law of total variance is often useful to look at a population divided into several groups so when all of the terms in an equation are all positive, then we can conclude that by conditioning theY, the variance of x would reduce on average, furthermore, we can say that the variance of a random variable is a measure of our uncertainty about the random variable.
Incorrect
The law of total variance is often useful to look at a population divided into several groups so when all of the terms in an equation are all positive, then we can conclude that by conditioning theY, the variance of x would reduce on average, furthermore, we can say that the variance of a random variable is a measure of our uncertainty about the random variable.
-
Question 19 of 30
19. Question
Which of the following is included in the steps required for the production of a useful simulation?
I. The possible outcomes should be described
II. The outcome of one or more random numbers should be linked to each other
III. The source of the random numbers should be chosen
IV. There should be no analysis of the simulated outcomes and then report the resultsCorrect
A simulation is only useful if it is mirrored to real-life outcomes. Several steps are required in producing a useful simulation. The steps required include: describing the possible outcomes, linkage of the outcomes of random numbers, choosing a source of random numbers, choosing a random number, noting the simulated outcomes based on the random number chosen, repeat the steps 4 and 5 multiple times until the outcome has a stable pattern and lastly, analyze the simulated outcomes and report the results.
Incorrect
A simulation is only useful if it is mirrored to real-life outcomes. Several steps are required in producing a useful simulation. The steps required include: describing the possible outcomes, linkage of the outcomes of random numbers, choosing a source of random numbers, choosing a random number, noting the simulated outcomes based on the random number chosen, repeat the steps 4 and 5 multiple times until the outcome has a stable pattern and lastly, analyze the simulated outcomes and report the results.
-
Question 20 of 30
20. Question
According to the illustration of a normal distribution, which of the following indicates the properties of a normal distribution?
I. It shows that in a normal distribution graph, the total area under the curve is 2
II. It shows that in a normal distribution, the curve in the center is symmetric
III. It shows that in a normal distribution, the mean and median are greater than the mode
IV. It shows that in a normal distribution, the area from the center to the right is equal to the area from the center to the leftCorrect
The properties of a normal distribution are:
The mean, median, and mode have all the same value
The curve in the center of the graph is symmetric
The area from the center to the right and from the center to the left is equal
The total area under the curve is 1Incorrect
The properties of a normal distribution are:
The mean, median, and mode have all the same value
The curve in the center of the graph is symmetric
The area from the center to the right and from the center to the left is equal
The total area under the curve is 1 -
Question 21 of 30
21. Question
In the book of Risk Modelling in General Insurance from Principles, which of the following are carried out using the statistical software package R?
I. Simulations
II. Statistical Analysis
III. Numerical Approximations
IV. Familiarity FunctionCorrect
Statistical software package R is a system where it has a diversity of codes and functions that can be used by the users. In risk modeling, simulations, statistical analysis, and numerical approximations are all being carried out using the statistical software package R.
Incorrect
Statistical software package R is a system where it has a diversity of codes and functions that can be used by the users. In risk modeling, simulations, statistical analysis, and numerical approximations are all being carried out using the statistical software package R.
-
Question 22 of 30
22. Question
Which of the following is included in the characteristics of statistics?
I. Most of the data in statistics are numerically expressed
II. Most of the data in statistics are collected in systematic order
III. Most of the data in statistics are an aggregation of facts
IV. Most of the data in statistics are collected with an undetermined purposeCorrect
All the statements about the characteristics of statistics are correct. The data stated in statistics are mostly numerically expressed as it mostly shows percentage or whole numbers. The collection of data is organized in systematic order as there is a process such as finding respondents or problems then afterward gathering the data and aggregation of facts to come up with an analysis. The collection of data in statistics is being done for a determined purpose which is to come up with an analysis and result of a tally for example.
Incorrect
All the statements about the characteristics of statistics are correct. The data stated in statistics are mostly numerically expressed as it mostly shows percentage or whole numbers. The collection of data is organized in systematic order as there is a process such as finding respondents or problems then afterward gathering the data and aggregation of facts to come up with an analysis. The collection of data in statistics is being done for a determined purpose which is to come up with an analysis and result of a tally for example.
-
Question 23 of 30
23. Question
Which of the following is true regarding the given formula of the cumulative distribution function?
I. The formula implies that the discrete random variable X is concentrated on the probability of getting a non-negative value
II. The function Fx is described as non-decreasing and right continuous.
III. The function Fx is a notation for the expected value of a random variable X
IV. The formula implies that the random variable X is independent and identically distributedCorrect
The given formula for the cumulative distribution function is Fx(x)=Pr[X≤x],x∈R. The function Fx is described as non-decreasing and right continuous which satisfies 0≤F_X (x)≤1 all x in R lim┬(n→→∞)〖F_X 〗 (x)=1 and lim┬(n→→∞)〖F_X 〗 (x)=0. The rest of the choices are incorrect as it describes the formula of another function.
Incorrect
The given formula for the cumulative distribution function is Fx(x)=Pr[X≤x],x∈R. The function Fx is described as non-decreasing and right continuous which satisfies 0≤F_X (x)≤1 all x in R lim┬(n→→∞)〖F_X 〗 (x)=1 and lim┬(n→→∞)〖F_X 〗 (x)=0. The rest of the choices are incorrect as it describes the formula of another function.
-
Question 24 of 30
24. Question
Which of the following is true regarding the possibilities in different degrees that an event would occur?
I. It is called a certain event if the likelihood of the occurrence of the event is sure and its probability is 1
II. It is called a possible event if the occurrence of the event would not happen at all and its probability is 1
III. It is called an impossible event if the occurrence of the event would not happen at all and its probability is 0
IV. The probabilities of all events that would or would not occur lie between 0 and 1Correct
Probability is focused on analyzing the likelihood of occurrence of an event. There are two possibilities which are called a certain event and an impossible event. A certain event has a probability of 1 which implies that the likelihood that event would occur is sure. An impossible event has a probability 0 which implies that the occurrence of the event would not happen. The probabilities of all the events would just be either 0 or 1 which implies that the event would or would not occur.
Incorrect
Probability is focused on analyzing the likelihood of occurrence of an event. There are two possibilities which are called a certain event and an impossible event. A certain event has a probability of 1 which implies that the likelihood that event would occur is sure. An impossible event has a probability 0 which implies that the occurrence of the event would not happen. The probabilities of all the events would just be either 0 or 1 which implies that the event would or would not occur.
-
Question 25 of 30
25. Question
In using statistics in risk modeling, which of the following are included in the assumptions that should already be done by the time of using statistics in the process?
I. It is assumed that the point estimation is already done in the study
II. It is assumed that all non-negative variables are already separated from negative variables
III. It is assumed that that the independent variables are already known
IV. It is assumed that the research has already come up with the hypothesis tests.Correct
According to the book of risk modeling in general principles, they had the assumption that the reader already knew about point estimations, properties of estimators, confidence intervals, and hypothesis tests. It is also assumed that the familiarity with plots such as histograms and quantile (or Q-Q) plots are known in addition to the familiarity with the empirical contribution function.
Incorrect
According to the book of risk modeling in general principles, they had the assumption that the reader already knew about point estimations, properties of estimators, confidence intervals, and hypothesis tests. It is also assumed that the familiarity with plots such as histograms and quantile (or Q-Q) plots are known in addition to the familiarity with the empirical contribution function.
-
Question 26 of 30
26. Question
Which of the following are taken as a prerequisite in studying risk modeling?
I. Probability
II. Statistics
III. Simulation
IV. Statistical software package RCorrect
Statistics and Simulation are taken as a prerequisite in risk modeling as the knowledge about the methods and ideas will be needed. Probability is the notation for basic quantities concerning the random variable X. Statistical software package R is a system that is being used where simulations, statistical analyses, and numerical approximations are being carried out.
Incorrect
Statistics and Simulation are taken as a prerequisite in risk modeling as the knowledge about the methods and ideas will be needed. Probability is the notation for basic quantities concerning the random variable X. Statistical software package R is a system that is being used where simulations, statistical analyses, and numerical approximations are being carried out.
-
Question 27 of 30
27. Question
Which of the following are one of the various possibilities for the expectation E[N]=∑_(k=0)^∞〖kPr(N=k)〗?
I. It may be finite
II. It may take the value +∞ or -∞
III. It may be a finite non-negative value
IV. It may not be definedCorrect
In a discrete random variable n taking values in N, the expectation is E[N]=∑_(k=0)^∞〖kPr(N=k). In the given expectation, various possibilities may occur: it may be infinite, it may take the value +∞ or -∞, or it may not be defined. The expectation of a non-negative random variable would just be either a finite non-negative value or +∞.
Incorrect
In a discrete random variable n taking values in N, the expectation is E[N]=∑_(k=0)^∞〖kPr(N=k). In the given expectation, various possibilities may occur: it may be infinite, it may take the value +∞ or -∞, or it may not be defined. The expectation of a non-negative random variable would just be either a finite non-negative value or +∞.
-
Question 28 of 30
28. Question
Which of the following are examples of transforms?
I. Probability generating functions
II. Variance generating functions
III. Moment generating functions
IV. Cumulant generating functionsCorrect
Both probability generating functions and moment generating functions are an example of transforms. Transforms are used for the calculation that involves the sum of independent random variables. Probability generating function is described as a series of presentation of probability mass function of a discrete random variable while moment generating function is used as an alternative route to analytical results instead of working directly with probability density function or cumulative distribution function.
Incorrect
Both probability generating functions and moment generating functions are an example of transforms. Transforms are used for the calculation that involves the sum of independent random variables. Probability generating function is described as a series of presentation of probability mass function of a discrete random variable while moment generating function is used as an alternative route to analytical results instead of working directly with probability density function or cumulative distribution function.
-
Question 29 of 30
29. Question
Which of the following are included in the main properties of the cumulative distribution function?
I. The function Fx of cumulative distribution is a non-decreasing function
II. The cumulative distribution function has an upward jump of size p_k at x_k k – 1
III. The cumulative distribution function can be replaced by the required function to be integrated
IV. Cumulative distribution function can be used as an unbiased estimatorCorrect
The three most important properties of cumulative distribution function: The function Fx of cumulative distribution is a non-decreasing function, like x→−∞x→−∞, the value of FX(x)FX(x) approaches 0 (or equals 0). That is, limx→−∞FX(x)=0limx→−∞FX(x)=0. This follows in part from the fact that Pr(∅)=0Pr(∅)=0. And as x→∞x→∞, the value of FX(x)FX(x) approaches 1 (or equals 1). That is, limx→∞FX(x)=1limx→∞FX(x)=1. This follows in part from the fact that Pr(E)=1Pr(E)=1. All of the properties mentioned above are applied equally to a discrete and continuous random variable.
Incorrect
The three most important properties of cumulative distribution function: The function Fx of cumulative distribution is a non-decreasing function, like x→−∞x→−∞, the value of FX(x)FX(x) approaches 0 (or equals 0). That is, limx→−∞FX(x)=0limx→−∞FX(x)=0. This follows in part from the fact that Pr(∅)=0Pr(∅)=0. And as x→∞x→∞, the value of FX(x)FX(x) approaches 1 (or equals 1). That is, limx→∞FX(x)=1limx→∞FX(x)=1. This follows in part from the fact that Pr(E)=1Pr(E)=1. All of the properties mentioned above are applied equally to a discrete and continuous random variable.
-
Question 30 of 30
30. Question
Which of the following is not true about the difference between the cumulative distribution function and probability density function?
I. The cumulative distribution function is the probability that the value of a random variable would be less than or equal to x while the probability density function is the probability that the value of the random variable has the value of x
II. Cumulative distribution function has a non-decreasing function while in probability density function, the probability of a single point is 0
III. Both discrete and continuous distributions are applied in the two functions
IV. There is no definite difference between the cumulative distribution function and probability density functionCorrect
The cumulative distribution function is the probability that the value of a random variable would be less than or equal to x. One of its properties is its function Fx is non-decreasing which implies that the value of the variable would not be less than 0. The probability density function is the probability that the value of a random variable would equal to the value of x. since it is a continuous distribution, its probability at a single point is equal to zero which is often expressed in terms of integration between two points. Both functions apply discrete or continuous distributions to the random variable.
Incorrect
The cumulative distribution function is the probability that the value of a random variable would be less than or equal to x. One of its properties is its function Fx is non-decreasing which implies that the value of the variable would not be less than 0. The probability density function is the probability that the value of a random variable would equal to the value of x. since it is a continuous distribution, its probability at a single point is equal to zero which is often expressed in terms of integration between two points. Both functions apply discrete or continuous distributions to the random variable.