59 Let X X X be a random sample from a uniform distribution

Last updated: 11/20/2023

59 Let X X X be a random sample from a uniform distribution on the interval 0 0 so that 0 x 0 0 0 otherwise f x Then if Y max X it can be shown that the rv U Y O has density function fu u foto nu 0 usl otherwise 0 a Use f u to verify that Y P a 2 1 a 2 1 and use this to derive a 100 1 a CI for 8 b Verify that P a Y 0 1 1 a and derive a 100 1 x CI for 0 based on this probability statement c Which of the two intervals derived previously is shorter If my waiting time for a morning bus is uniformly distributed and observed waiting times are x 4 2 x 3 5 x3 1 7 x 1 2 and x 2 4 derive a 95 CI for 0 by using the shorter of the two intervals 1