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Coin flipping and probability

Random Variable

Random Variable

Lifer
Keep flipping a coin until you get a heads and then a tails on consecutive flips.

Let X equal the number of flips needed to get a heads-tails

therefore P(X)= (x-1)/2^x for x = 2,3,4,...

But how would you figure out the mean and variance of X? I'm having a miserable time trying to find the moment-generating function for X.



 
Screw the math. The odds are 1 set out of every 4 flips. (1/2 * 1/2 = 1/4) 1/2 odds that a flip is heads, and 1/2 that the next flip is tails.
 
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