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## Homework Statement

Let X be a random variable with distribution function px(x) defined by:

p

_{x}(0) = a and p

_{x}(x) = P

_{x}(-x) = ((1-a)/2)*p*(1-p)^(x-1), x = 1,2...

where a and p are two constants between 0 and 1, and p

_{x}(0) is meant to be the probability that X=0

a) What is the mean of X?

b) Use the variance of a geometric random variable to compute the variance of X.

## The Attempt at a Solution

Okay so for a) I just used the geometric random variable formula, but made ((1-a)/2) = b. Since the mean of a geometric random variable with probability of success p is E(X) = 1/p, I just multiplied it by b, giving me -(a-1)/2p. Is this correct?

Also, I have no idea how to do part b), if anyone could help me with it I'd appreciate it.

Thanks in advance.