For another approach to Theoretical Exercise 1, let Tr denote the number of flips required...

For another approach to Theoretical Exercise 1, let Tr denote the number of flips required to obtain a run of r consecutive heads.

(a) Determine .

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(b) Determine E[Tr] in terms of E[Tr−1].

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(c) What is E[T1]?

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(d) What is E[Tr]?

Exercise 1

A coin that lands on heads with probability p is continually flipped. Compute the expected number of flips that are made until a string of r heads in a row is obtained.

Simplify and solve for E[X]