X and Y are two random variables. X is a gaussian random variable with mean 0 and variance 4. Y is a bernoulli random variable with parameter p. Let random variables Z, H, R and L be defined as...
$$Z = X + Y$$
$$H = XY$$
$$R = X^Y$$
$$L = X^3 + Y^3$$
Determine E[Z], E[H], E[R], and E[L]
I've been stumped on this one for a while and just really don't know where to get started. I know E[X] is 0 and E[Y] should be p, but I'm not sure how to apply that to these four variables Z H R and L. Any help would definitely be appreciated!
EDIT: I believe I am allowed to assume X and Y are independent from each other.