Consider the following statements:

i. The mean and variance of a Poisson random variable are equal.
ii. For a standard...

Question

Consider the following statements:

i.  The mean and variance of a Poisson random variable are equal.
ii. For a standard normal random variable, the mean is zero and the variance is one.

Which ONE of the following options is correct?

A. Both (i) and (ii) are true
B. (i) is true and (ii) is false
C. (i) is true and (ii) is false
D. Both (i) and (ii) are false

Accepted Answer

Both statements are true. Answer A. Statement i is a fundamental property of the Poisson distribution: if X ~ Poisson(lambda), then E[X] = lambda and Var(X) = lambda, so mean equals variance. Statement ii defines the standard normal distribution N(0,1): by definition its mean is 0 and its variance is 1. Both statements are true, so the answer is A.