•IfXis exponential with parameterλ, such thatfX(x) =λexp(-λx), showthat the ‘ceiling’ ofX(i.e., the next integer, so that the integer of 1.1 is2, the integer of 2.4 is 3 etc)Yhas geometric distribution with parameterp= 1-exp(-λ).Hint: ConsiderP(Y= 1) =P(0< X <1), generalizefor anyi, and compare with the pmf of the geometric which isP(Y=i) =p(1-p)i-1.•IfX1, . . . , Xnare exponentially distributed such thatfXi(x) =λexp(-λx),show that the distribution ofY= min(X1, . . . , Xn)is exponential with pa-rameternλ, so thatfY(y) =nλexp(-nλy).Hint: In order formin(X1, . . . , Xn)> y, we need ALL of them to beGREATER thany. What’s the probability that none are less than
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