2.3-16. 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. HINT: Draw a tree diagram. 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.

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2.3-16. 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. HINT: Draw a tree diagram.
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).
Transcribed Image Text:2.3-16. 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. HINT: Draw a tree diagram. 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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