Question

1. Suppose X follows the normal distribution with mean μ and variance σ^2 . Then:

(Circle all that apply.)

A. X is symmetric with respect to the y-axis.

B. P(X=2)=P(X=-2).

C. Y=aX follows the same distribution as X, where a is a constant.

D. None of the above statements is correct.

2.

Given a random variable X having a normal distribution with μ=50, and σ=10. The probability that Z assumes a value between 45 and 62 is: ___________.

3. Which of the following statements is true?

A. The Gamma distribution is a special case of the exponential distribution.

B. The Exponential distribution is used to describe the number of arrivals

within one unit.

C. The expectation of the exponential distribution does not equal to that of

the Poisson distribution in general.

D. All of the above is correct.

Answer 1

1. Suppose X follows the normal distribution with mean μ and variance σ^2 . Then:

A. X is symmetric with respect to the y-axis.

B. P(X=2)=P(X=-2).

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2:

3:

Exponential distribution is a specila case of Gamma distribution. So A is false.

Poisson distribution  is used to describe the number of arrivals within one unit. So B is false.

C. The expectation of the exponential distribution does not equal to that of the Poisson distribution in general. This is true.

The rate of the exponential distribution does not equal to that of the Poisson distribution in general.