what does px(0) = a and px(x) = Px(-x) mean?
Is px(0) the probability that X=0?
and is this symmetric about 0, with the px(x) = Px(-x)?
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.
a) What is the mean of X?
b) Use the variance of a geometric random variable to compute the variance of X.
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? If it is correct then I'm pretty sure I know how to do part b), so if anyone could help me with this I'd really appreciate it.
Thanks in advance.
Yup, px(0) is meant to be that the probability that X=0, and I *think* it is meant to be symmetric about 0 (with px(x) = Px(-x)). Do they play some part in the mean of X? (I didn't really take them into account when I tried to work out the mean because I didn't think they were important...).