y to show this is to use P(X > a) P(X + c-a+ c) for any constant number of custo

Question

y to show this is to use P(X > a) P(X + c-a+ c) for any constant number of customers visiting a store during a day is a random variable with mean a) Using Chebyshev's inequality, find an upper bound for having more than 120 or less Hint: One wa cER 22. The EX = 100 and variance Var(X) 225. than 80 customers in a day. That is, find an upper bound on P(X 80 or X 120). (b) Using the one-sided Chebyshev inequality (Problem 21), find an upper bound for having more than 120 customers in a day. aIsing Chernoff bounds find an upper bound

Explanation / Answer

22) a here std deviaiton =(225)1/2 =15

threfore 80 and 120 falls k= (20/15)=4/3 std deviation away from mean

threfore from Chebyshev's P(X<80 or X>120)=1-P(80<X<120)=1-(1-1/k2) =1/(4/3)2 =9/16 =0.5625

b) P(X>120)=1/2k2 =1/(2*(4/3)2) =9/32=0.28125

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