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Problem 5. (5 pts) Expectation Trick, Strong Law and the CLT (a) (2 pts) Let X be the number of fixed points in a random perm

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soluation :- a) Let & be the fixed point Hence X~POB (A) P (x-x) = 1=0, 1,2.. th 2 a = Mean e=2.71821 We know that E(X)=2=1=

C) P (31000 3500 | 55002255) = P (51000 500) P (ssoo >255) -(500) = eno a(255) = e (500-255) en (245) But 2-1 -245 P (51000 2

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