Desperate! Help! 3 Probability Questions

1. Let Y ~ Binomial(n,p) with pmf pY(y).Obtain the value of y for which pY(y) is maximum.

2. Let Y ~ geometric(p) with pmf pY(y).

(a) Show that the value p = 1/y maximizes the pmf.

(b) Obtain E(1/Y ).

3. Let X be a random variable, and Y = aX + b for non-random values a and b. Using the fact that MY(t) = (e^bt)MX(at) show that V ar(Y ) = (a^2)V ar(X).

Man...I'm so stressed. The textbook is useless and the prof won't answer questions till all 10 questions are handed in tomorrow. These are the last 3 questions I have.

Thanks in advance!