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Question: What can be said about the pair of events A={1,2,3} and B={4,5} relative to the sample space S={1,2,3,4,5,6} associated with rolling a fair six-sided (6-sided) die?

13 Feb 2023,7:40 AM


Question 1

What can be said about the pair of events A={1,2,3} and B={4,5} relative to the sample space S={1,2,3,4,5,6}associated with rolling a fair six-sided (6-sided) die?

o   They are neither mutually exclusive nor exhaustive.

o   They are both mutually exclusive and exhaustive.

o   They are mutually exclusive, but not exhaustive.

o   They are exhaustive, but not mutually exclusive.

 

 

Question 2

What can be said about the pair of events A={1,2,3} and B={3,4,5,6} relative to the sample space S={1,2,3,4,5,6}associated with rolling a fair six-sided (6-sided) die?

o   They are exhaustive, but not mutually exclusive.

o   They are both mutually exclusive and exhaustive.

o   They are neither mutually exclusive nor exhaustive.

o   They are mutually exclusive, but not exhaustive.

 

 

Question 3

What can be said about the pair of events A={1,3} and B={3,5,6} relative to the sample space S={1,2,3,4,5,6}associated with rolling a fair six-sided (6-sided) die?

o   They are mutually exclusive, but not exhaustive.

o   They are neither mutually exclusive nor exhaustive.

o   They are both mutually exclusive and exhaustive.

o   They are exhaustive, but not mutually exclusive.

 

 

Question 4

What can be said about the pair of events A={1,2,3} and B={4,5,6} relative to the sample space S={1,2,3,4,5,6}associated with rolling a fair six-sided (6-sided) die?

o   They are neither mutually exclusive nor exhaustive.

o   They are both mutually exclusive and exhaustive.

o   They are mutually exclusive, but not exhaustive.

o   They are exhaustive, but not mutually exclusive.

 

 

Question 5

What are the odds in favor of an event A that satisfies P(A)=0.2?

o   0.2

o   4

o   5

o   0.25

 

 

Question 6

Let X and Y be random variables satisfying E[X]=2 and E[Y]=3, respectively.  What is the value of the expectation E[X+2Y]?

o   8

o   14

o   The answer cannot be determined from the given information.

o   7

 

 

Question 7

Let X and Y be random variables satisfying V[X]=2 and V[Y]=3, respectively.  What is the value of the variance V[X+2Y]?

o   7

o   14

o   8

o   The answer cannot be determined from the given information.

 

 

Question 8

Let X be a random variable satisfying V[X]=5.  What is the value of the variance V[3X]?

o   75

o   The answer cannot be determined from the given information.

o   45

o   15

 

 

Question 9

Consider the random variable X representing a randomly-chosen individual's bank account number. Which of the following statements is true of X?

o   It is a continuous quantitative data variable.

o   It is a discrete quantitative data variable.

o   It is not a data variable.

o   It is a qualitative or categorical data variable.

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Expert answer


Question 1

What can be said about the pair of events A={1,2,3} and B={4,5} relative to the sample space S={1,2,3,4,5,6}associated with rolling a fair six-sided (6-sided) die?

o   They are neither mutually exclusive nor exhaustive.

o   They are both mutually exclusive and exhaustive.

o   They are mutually exclusive, but not exhaustive.

o   They are exhaustive, but not mutually exclusive.

 

 

Question 2

What can be said about the pair of events A={1,2,3} and B={3,4,5,6} relative to the sample space S={1,2,3,4,5,6}associated with rolling a fair six-sided (6-sided) die?

o   They are exhaustive, but not mutually exclusive.

o   They are both mutually exclusive and exhaustive.

o   They are neither mutually exclusive nor exhaustive.

o   They are mutually exclusive, but not exhaustive.

 

 

Question 3

What can be said about the pair of events A={1,3} and B={3,5,6} relative to the sample space S={1,2,3,4,5,6}associated with rolling a fair six-sided (6-sided) die?

o   They are mutually exclusive, but not exhaustive.

o   They are neither mutually exclusive nor exhaustive.

o   They are both mutually exclusive and exhaustive.

o   They are exhaustive, but not mutually exclusive.

 

 

Question 4

What can be said about the pair of events A={1,2,3} and B={4,5,6} relative to the sample space S={1,2,3,4,5,6}associated with rolling a fair six-sided (6-sided) die?

o   They are neither mutually exclusive nor exhaustive.

o   They are both mutually exclusive and exhaustive.

o   They are mutually exclusive, but not exhaustive.

o   They are exhaustive, but not mutually exclusive.

 

 

Question 5

What are the odds in favor of an event A that satisfies P(A)=0.2?

o   0.2

o   4

o   5

o   0.25

 

 

Question 6

Let X and Y be random variables satisfying E[X]=2 and E[Y]=3, respectively.  What is the value of the expectation E[X+2Y]?

o   8

o   14

o   The answer cannot be determined from the given information.

o   7

 

 

Question 7

Let X and Y be random variables satisfying V[X]=2 and V[Y]=3, respectively.  What is the value of the variance V[X+2Y]?

o   7

o   14

o   8

o   The answer cannot be determined from the given information.

 

 

Question 8

Let X be a random variable satisfying V[X]=5.  What is the value of the variance V[3X]?

o   75

o   The answer cannot be determined from the given information.

o   45

o   15

 

 

Question 9

Consider the random variable X representing a randomly-chosen individual's bank account number. Which of the following statements is true of X?

o   It is a continuous quantitative data variable.

o   It is a discrete quantitative data variable.

o   It is not a data variable.

o   It is a qualitative or categorical data variable.

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