1) Let Y have pdf:

fy(y) = y, between 0 and 1 (inclusive), 2-y, between 1 and 2 (inclusive), and 0 everywhere else.

Find My(t)

2) Fined E(Y^4) if Y is an exponential random variable with fy(y) = xe^(-xy), y > 0

3) Find the variance of Y if My(t) = e^-2t/(1-t^2)

4) Calculate P(X less than or equal to 2) if Mx(t) = (1/4 + 3/4e^t)^5