Let X be a random variable with distribution function px(x) defined by:
px(0) = a and px(x) = Px(-x) = ((1-a)/2)*p*(1-p)^(x-1), x = 1,2...
where a and p are two constants between 0 and 1, and px(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.