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The hatcheck staff has had a long day, and at the end of the party they decide to return people’s hats at random. Suppose that npeople have their hats returned at random. We previously showed that the expected number of people who get their own hat back is 1, irrespective of the total number of people. In this problem we will calculate the variance in the number of people who get their hat back.Let Xi= 1if the ith person gets his or her own hat back and 0 otherwise. Let Sn::= n i=1 Xi, so Snis the total number of people who get their own hat back. Show that (a) E [Xi2] = 1/n.

The hatcheck staff has had a long day, and at the end of the party they decide to return people’s hats at random. Suppose that npeople have their hats returned at random. We previously showed that the expected number of people who get their own hat back is 1, irrespective of the total number of people. In this problem we will calculate the variance in the number of people who get their hat back.Let Xi= 1if the ith person gets his or her own hat back and 0 otherwise. Let Sn::= n i=1 Xi, so Snis the total number of people who get their own hat back. Show that (a) E [Xi2] = 1/n.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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The hatcheck staff has had a long day, and at the end of the party they decide to return people’s hats at random. Suppose that npeople have their hats returned at random. We previously showed that the expected number of people who get their own hat back is 1, irrespective of the total number of people. In this problem we will calculate the variance in the number of people who get their hat back.Let Xi= 1if the ith person gets his or her own hat back and 0 otherwise. Let Sn::= n i=1 Xi, so Snis the total number of people who get their own hat back. Show that (a) E [Xi2] = 1/n.

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