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Exercise 2. C What is the expected number of Tails until I get the third Heads in an infinite sequence of independent coin to

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Answer #1

For the fair coin, we are given here that
P(heads) = P(tails) = 1/2 = 0.5

Therefore the expected number of total tosses required to get the third heads is computed using the expected value of the negative binomial distribution here as:

= n/p = 3/(1/2) = 6

As the expected number of total tosses required to get 3 heads is 6, therefore total expected number of tails before the 3 heads would be computed as:
= 6 - 3 = 3

Therefore 3 is the expected number of tails here.

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