here's what I got for my first question:
=> true, since E(X) = p for RV ~ Bernoulli(p)
Suppose X1 and X2 are stoch. indep. Bernoulli RVs with params p1 and p2 respectively. Let Y = X1X2 and W = X1 + X2. I need to determine whether the following statements are true or false so just give me a clue please, I'd like to work it out myself. If no tip can be given without giving it away please say so.
1. the RV Y ~ Bernoulli(p_1p_2)
2. What is the general formula for finding the variance of a RV of the form Z = XY (X and Y both RVs).
Thanks in advance.
I found the formula for the second question.
The problem wanted me to prove that given X,Y indep. and Z=XY
and the formula I found was
and from here the answer is obvious given that Cov(X,Y)=0.
However, I'd like to know how the formula for V(XY) is derived.