(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.
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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).
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and find the cdf of Y:
 = \Pr(\ln U \geq - y) = \Pr(U \geq e^{-y}) = \int_{e^{-y}}^1 1 \, du)
.
for
and zero elsewhere, as required.
