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Distribution with indicator random variables


New member
Sep 13, 2009
a) Let A and B be independent events, with indicator random variables I[sub:92pwfhv3]A[/sub:92pwfhv3] and I[sub:92pwfhv3]B[/sub:92pwfhv3]. Describe the distribution of (I[sub:92pwfhv3]A[/sub:92pwfhv3] + I[sub:92pwfhv3]B[/sub:92pwfhv3])[sup:92pwfhv3]2[/sup:92pwfhv3] in terms of P(A) and P(B). What is E(I[sub:92pwfhv3]A[/sub:92pwfhv3] + I[sub:92pwfhv3]B[/sub:92pwfhv3])[sup:92pwfhv3]2[/sup:92pwfhv3]?

I know the E(I[sub:92pwfhv3]A[/sub:92pwfhv3]) = P(A), but I don't know how you would use this to find the distribution.
Is the expectation simply P(A)[sup:92pwfhv3]2[/sup:92pwfhv3] + 2*P(A)*P(B) + P(B)[sup:92pwfhv3]2[/sup:92pwfhv3]?

b) Suppose that X is a random variable with just two possible values a and b. For x = a and b find a formula for p(x) = P(X = x) in terms of a, b and mu = E(X).

Thanks for any help!