Thread: Two questions

(1) show that -log(U) is exponential(1) if U is uniform(0,1)

(2)Let X be exponential(2). Set Y=1-exp(-2Y) . Show Y is uniform(0,1)

I thinks these two are quite similar. But I still dont know how to solve it. Anyone can? thx.

Originally Posted by solskjaer

(1) show that -log(U) is exponential(1) if U is uniform(0,1)

[snip]

Let and find the cdf of Y:



noting that

.

Then for and zero elsewhere, as required.


You should re-try (2).