Hi! I've got a few problems that I wonder if someone could help me with.

1) If Y is a discrete random variable that assigns positive probabilites to only the positive integers, show that.

I don't have a clue about how to solve this one.

2) Let Y denote a geometric random variable with probability of success p.

a) Show that for a positive integer a,

b) Show that for positive integers a and b

I've been trying a lot with this one, but don't really know how to prove this.

3) Find E[Y(Y-1)] for a geometric random variable Y by finding d^2/dq^2 for

I don't know about this one either. My suggestion is that the second derivative is equal to this:

, but how do I use that to find E[Y(Y-1)]?

Would be nice if someone could help me with any of these problems.