Given , suppose X is a random variable with and E{X}=1. Definite by Q(A)= . Show that if P(A) = 0, then Q(A)=0. Give an example that shows that Q(A)=0 does not in general imply P(A)=0.

I'm pretty sure that , so I was thinking that maybe we could break Q(A) up into . However, this would be assuming that X and 1_A are independent random variables? Would this be true? If so, then it's very obvious why, if P(A)=0, then Q(A)=0. Anyone have any hints? Thanks!