"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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Show that the expected value of îN is p.

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Question

"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 \( N \).

Expert Solution

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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