Question

A fair coin is continually flipped until heads appears for the 10th time. Let X denote the number of tails that occur. Compute the probability mass function and the expected value of X.

Answer 1

P (X = i) = (i + 9 _ 9) (1/2)^(i + 10)

Explanation:

Range of X = {0, 1, 2, 3......10}

P (X = i) = P (NB (10, ½) i = 10)

P (X = i) = (i + 9 _ 9) (1/2)^10 (1/2)^(1+10-10)

P (X = i) = (i + 9 _ 9) (1/2)^10 (1/2)^1

P (X = i) = (i + 9 _ 9) (1/2)^(i + 10)