Let U have a U(0, 1) distribution. Show that Z = 1 − U has a U(0, 1) distribution by deriving the probability density function or the distribution function. 2. We have seen that if U has a U(0, 1)...

Let U have a U(0, 1) distribution. Show that Z = 1 − U has a U(0, 1) distribution by deriving the probability density function or the distribution function.

2. We have seen that if U has a U(0, 1) distribution, then X = − lnU has an Exp(1) distribution. Check this by verifying that P(X ≤ a)=1 − e−a for a ≥ 0.