70. Suppose the cdf F(x) is strictly increasing and let F1(y) denote the inverse function for 0  y  1.

Show that the distribution of F[Yi] is the same as the distribution of the ith smallest order statistic from a uniform distribution on (0, 1). Hint: Start with P[F(Yi)

y] and apply the inverse function to both sides of the inequality. Note: This result should not be surprising to you, since we have already noted that F(X) has a uniform distribution on (0, 1). The result also holds when the cdf is not strictly increasing, but then extra care is necessary in de ning the inverse function.