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  3. problem 01 let x be the number of people who...

Question: problem 01 let x be the number of people who...

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Problem 0.1 Let X be the number of people who enter a bank by time t>0. Suppose ke-t k! for k 0,1,2,., and for t>s > 0, and k-r=0,1,2, . . . . (a) Find Pr(X2 = k | X,-1) for k = 0, 1, 2, . . . . (b) Find E[X2 X1-1 Useful information: Dont eat yellow snow, and et-L=0 tk/k! Problem 0.2 Recall the Geometric(p) distribution where Xnumber of flips of a coin until you get a head (H) with Pr(H . The distribution is for x 1,2,..., with mean E(X)1x(1-p)p 1/p, which can be obtained by brute force. An easier way to find the mean is to condition on the first toss, say Y mean is 1 /p using E(X) = EE( Y). 0 or 1 if the first toss is T or H. Show the

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