Get answer: Probability A fair coin is tossed repeatedly. The probability that the first
Chapter 9, Problem 39(choose chapter or problem)
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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