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Solved: Each of n 2 people puts his or her name on a slip of paper (no two have the same
Chapter 7, Problem 46(choose chapter or problem)
Each of n 2 people puts his or her name on a slip of paper (no two have the same name). The slips of paper are shued in a hat, and then each person draws one (uniformly at random at each stage, without replacement). Find the standard deviation of the number of people who draw their own names.
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QUESTION:
Each of n 2 people puts his or her name on a slip of paper (no two have the same name). The slips of paper are shued in a hat, and then each person draws one (uniformly at random at each stage, without replacement). Find the standard deviation of the number of people who draw their own names.
ANSWER:Step 1 of 5
Let be a random variable that marks the number of people that have draws their own names out of the hat. Let be the indicator random variable that marks whether th person has drawn his/her name or not. We know that since all names are equally likely to be drawn out of the hat. Similarly, we have that for .