Question

Observe independent flips of a fair coin until heads occurs twice. Let X1X_{1} equal the number of flips up to and including the first H. Let X2X_{2} equal the number of additional flips up to and including the second H. Let Y=X1X2Y=X_{1}-X_{2}. Find E[Y] and Var[Y]. Hint: Don't try to find PY(y)P_{Y}(y).

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