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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). Solution.

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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). Solution

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  • 1. 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). Solution