In Section 3.6.3, we saw that if U is a random variable that is uniform on (0, 1)

and if, conditional on U = p,X is binomial with parameters n and p, then

For another way of showing this result, let U,X1,X2, . . . , Xn be independent uniform (0, 1) random variables. Define X by X = #i: Xi

(a) What is P{X = i}?

(b) Explain how this proves the result of Section 3.6.3.

Transcribed Image Text:

1 P{X i}=- i = 0, 1,...,n n+1'