Let y1, y2,... , yn denote a random sample of size n from a population with a uniform distribution on the interval (0,theta). let y(n) = max{y1,y2,...,yn} and u = (1/theta)y(n). (a) show that u has distribution function fu(u) = { (b) because the distribution of u does not depend on theta, u is a pivot. find a 95% lower confidence hound for theta.

Will mark kayla wants to find the width, ab, of a river. she walks along the edge of the river 65 ft and marks point c. then she walks 25 ft further and marks point d. she turns 90° and walks until her location, point a, and point c are collinear. she marks point e at this location, as shown (a) can kayla conclude that δabc and δedc are similar? why or why not? (b) suppose de = 15 ft. what can kayla conclude about the width of the river?