What you have done looks correct to me.
I do agree it is a bit of a confusing question.
I guess this question can go in either this section or analysis... I'll put it here.
Let A = {a,b,c}, F = and P be a probability measure such that:
P({a})=1/2 P({b})=1/6 P({c})=2/6, then (A,F,P) is a probability space.
Define Y:A-->R as Y(w) = 1 if w = a or c and Y(w) = 0 if otherwise.
Let be the probability distribution of Y
Find
My problem is I'm not really sure what this integral represents. It looks like it should just be the expected value of Y, but I'd prefer to calculate it directly.
What I have is that since X(w) can only take 2 values, 0 and 1, we have that answer is
Any thoughts?