# Question

Let X equal the number of flips of a fair coin that are required to observe the same face on consecutive flips.

(a) Find the pmf of X.

(b) Find the moment-generating function of X.

(c) Use the mgf to find the values of

(i) The mean and

(ii) The variance of X.

(d) Find the values of

(i) P(X ≤ 3),

(ii) P(X ≥ 5), and

(iii) P(X = 3).

(a) Find the pmf of X.

(b) Find the moment-generating function of X.

(c) Use the mgf to find the values of

(i) The mean and

(ii) The variance of X.

(d) Find the values of

(i) P(X ≤ 3),

(ii) P(X ≥ 5), and

(iii) P(X = 3).

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