A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN: 9780134753119
Author: Sheldon Ross
Publisher: PEARSON
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Question
"Show that the expected value of \(\hat{p}_N\) is \(p\)."
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Transcribed Image Text:"Show that the expected value of \(\hat{p}_N\) is \(p\)."
Suppose you want to find out how many people support Policy \( X \). A standard polling approach is to just ask \( N \) many people whether or not they support Policy \( X \), and take the fraction of people who say yes as an estimate of the probability that any one person supports the policy. Suppose that the probability someone supports the policy is \( p \), which you do not know. Let \( \hat{p}_N \) be the number of people polled who supported the policy, divided by the total number of people polled \( N \).
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Transcribed Image Text:Suppose you want to find out how many people support Policy \( X \). A standard polling approach is to just ask \( N \) many people whether or not they support Policy \( X \), and take the fraction of people who say yes as an estimate of the probability that any one person supports the policy. Suppose that the probability someone supports the policy is \( p \), which you do not know. Let \( \hat{p}_N \) be the number of people polled who supported the policy, divided by the total number of people polled \( N \).
Expert Solution
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Step 1

Given that p denote the probability that someone aupports the policy.

And X denote the nunber of persons support Policy, out of N persons.

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