Let be a random sample from a uniform distribution on the interval [0, u], so that Then if , it can be shown that the rv has density function

a. Use to verify that and use this to derive a % CI for u.

b. Verify that , and derive a % CI for u based on this probability

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 x1 4.2, , and , derive a 95% CI for u by using the shorter of the two intervals.