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A coin that when Hipped comes up heads with probability p

Chapter 4, Problem 3STE

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QUESTION:

Problem 3STE

A coin that when Hipped comes up heads with probability p is flipped until either heads or tails has occurred twice. Find the expected number of flips.

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QUESTION:

Problem 3STE

A coin that when Hipped comes up heads with probability p is flipped until either heads or tails has occurred twice. Find the expected number of flips.

ANSWER:

Solution:

Step 1 of 1:

We have to find the expected number of flips.  

     Let X denote number of flips.

     We get the pmf of X as

         When we need 2 plips,

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