Get answer: Probability A fair coin is tossed repeatedly. The probability that the first

Chapter 9, Problem 39

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A fair coin is tossed repeatedly. The probability that the first head occurs on the  nth toss is   \(P(n)=\left(\frac{1}{2}\right)^{n}\). When this game is repeated many times, the average number of tosses required until the first head occurs is

                                        \(E(n)=\sum_{n=1}^{\infty} n P(n)\).

(This value is called the expected value of  n.) Use the results of Exercises 35 - 38 to find  E(n). Is the answer what you expected? Why or why not?

Text Transcription:

P(n) = (1 / 2)^n

E(n) = sum_{n = 1}^{infty} n P(n)

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