Question

In Exercise 6.2.15, you showed that, for the hat check problem, the number $S_n$ of people who get their own hats back has $E\left(S_n\right)=V\left(S_n\right)=1$. Using Chebyshev's Inequality, show that $P\left(S_n \geq 11\right) \leq .01$ for any $n \geq 11$.

   In Exercise 6.2.15, you showed that, for the hat check problem, the number $S_n$ of people who get their own hats back has $E\left(S_n\right)=V\left(S_n\right)=1$. Using Chebyshev's Inequality, show that $P\left(S_n \geq 11\right) \leq .01$ for any $n \geq 11$.

Probability and statistics

Robert E. K. Rourke,… 1st Edition

Chapter 8, Problem 9

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In Exercise 6.2.15, you showed that, for the hat check problem, the number $S_n$ of people who get their own hats back has $E\left(S_n\right)=V\left(S_n\right)=1$. Using Chebyshev's Inequality, show that $P\left(S_n \geq 11\right) \leq .01$ for any $n \geq 11$.

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