Let U1,U2, . . . be a sequence of independent uniform(0,
Chapter 7, Problem 7.62(choose chapter or problem)
Let U1,U2, . . . be a sequence of independent uniform(0, 1) random variables. In Example 5i weshowed that, for 0 x 1,E[N(x)] = ex, whereN(x) = minn :ni=1Ui > xThis problem gives another approach to establishingthat result.(a) Show by induction on n that, for 0 < x 1and all n 0,P{N(x) n + 1} = xnn!Hint: First condition on U1 and then use theinduction hypothesis.Use part (a) to conclude thatE[N(x)] = ex
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