(solution) Assignment set 5 Let U be a standard uniformly distributed random

(solution) Assignment set 5 Let U be a standard uniformly distributed random

Assignment set 5

  1. Let U be a standard uniformly distributed random variable and N be a standard normally distributed random variable. Show that, for any x, the random variable ??1(U + (1 ? U)?(x)) has the same distribution function as N given N > x. Here ? is the cumulative distribution function of the standard normal distribution and ??1 its inverse. (This fact can be exploited to simulate normal random variables conditioned to exceed some level x.)