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

Unfortunately, we don't have that question answered yet. But you can get it answered in just 5 hours by Logging in or Becoming a subscriber.

Becoming a subscriber
Or look for another answer

×

Login

Login or Sign up for access to all of our study tools and educational content!

Forgot password?
Register Now

×

Register

Sign up for access to all content on our site!

Or login if you already have an account

×

Reset password

If you have an active account we’ll send you an e-mail for password recovery

Or login if you have your password back