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Question: Consider the random variable X representing the randomly-determined result of a single flip of an unfairly-weighted coin

16 Feb 2023,2:32 PM


Question 1

Consider the random variable X representing the randomly-determined result of a single flip of an unfairly-weighted coin. The random variable X is most likely to be distributed according to which of the following discrete probability distributions?

o   Binomial Distribution

o   Poisson Distribution

o   Geometric Distribution

o   Bernoulli Distribution

 

 

Question 2

Consider the random variable X representing the randomly-determined number of heads resulting from a sequence of five flips of an unfairly-weighted coin.  The random variable X is most likely to be distributed according to which of the following discrete probability distributions?

o   Bernoulli Distribution

o   Poisson Distribution

o   Geometric Distribution

o   Binomial Distribution

 

 

Question 3

Consider the random variable X representing the randomly-determined trial number of the first head resulting from an unending sequence of flips of an unfairly-weighted coin.  The random variable X is most likely to be distributed according to which of the following discrete probability distributions?

o   Poisson Distribution

o   Geometric Distribution

o   Bernoulli Distribution

o   Binomial Distribution

 

 

Question 4

Consider the random variable X representing the randomly-determined number of fish caught while fishing on a particular lake on a given day.  The random variable X  is most likely to be distributed according to which of the following discrete probability distributions?

o   Bernoulli Distribution

o   Geometric Distribution

o   Poisson Distribution

o   Binomial Distribution

 

 

Question 5

Let X be a random variable satisfying E[X]=2 and V[X]=9.  What is the value of the variance V[X¯(1)] of the sampling distribution of the sample mean X¯(1) generated from all possible samples of n=1 observation of X?

o   0.2

o   3

o   The answer cannot be determined from the given information.

o   9

 

 

Question 6

Let X be a random variable satisfying E[X]=2 and V[X]=9.  What is the value of the variance V[X¯(3)] of the sampling distribution of the sample mean X¯(3) generated from all possible samples of n=3 observations of X?

o   9

o   3

o   0.2

o   The answer cannot be determined from the given information.

 

 

Question 7

Let X be a random variable satisfying E[X]=2 and V[X]=9.  What is the value of the variance V[X¯(45)] of the sampling distribution of the sample mean X¯(45) generated from all possible samples of n=45 observations of X?

o   0.2

o   9

o   3

o   The answer cannot be determined from the given information.

 

 

Question 8

Let X be a normally distributed random variable satisfying E[X]=2 and V[X]=9.  What is the value of the variance V[X¯(3)] of the sampling distribution of the sample mean X¯(3) generated from all possible samples of n=3 observations of X?

 

o   9

o   0.2

o   The answer cannot be determined from the given information.

o   3

 

 

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