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We toss a coin randomly and define

Y := { X if the coin toss is heads

.......{ 1 is the coin toss is tails

Question wants the Var(Y^p) for any p > 0.

My work:

Var(Y^p) = E(Y^(2p)) - E(Y^p)^2

I'm not sure how to go about finding E(Y^p) and E(Y^(2p)). I thought of using moment generating functions, but the preferred method is supposed to utilize conditional probabilities. Any hint on how to compute E(Y^p) would help.

Thanks