610 Chapter 14*:Life Testing
(b) Use part (a) to show thatE[U(i)]=i/(n+1). [Hint:To evaluate the
resulting integral, use the fact that the density in part (a) must integrate to 1.]
(c) Use part (b) and Problem 28a to conclude thatE[F(X(i))]=i/(n+1).
30.IfU is uniformly distributed on (0, 1), show that−logUhas an exponen-
tial distribution with mean 1. Now use Equation 14.3.7 and the results of the
previous problems to establish Equation 14.5.7.