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!
No. What is true is that if and else. Remember is an event, not a subset of .
For instance (you should write this more formally), suppose we toss a fair coin, and define the event and is defined to be 0 in case heads shows up, and to be 2 if tails shows up. Then what are , and ?