I'm not sure if this actually Advanced, but it is from a 3000-level University course. My apologies if I am misposting.

Ok... So that seems pretty clear to me that p = .4 (based on the logic that q=.6 = 1-p).A random variable X has the probability mass function

, for x = 1, 2 , 3, …

Find p, the mean and the variance of X.

But I have no idea where to go from here. If I go to take the mean and variance, according to the text and notes, the formulae I'd be using are:

and

Maybe my calculus-fu has weakened (it's been a long time), but I can't for the life of me figure out how to do those sums since they don't appear to resemble any of the series I studied in Calc II...

If anyone could give me a pointer, or tell me where I did something wrong, I'd appreciate it. Thanks...