Let Y have the probability density function:

f(y)= (3-2y)/2^2 , 0 y

f(y)= 0, otherwise

a. Show that Y has distribution functions

F(y)= 0, y 0

F(y)= (3y-y^2)/2^2, 0 y

F(y)= 0, y >

b. Show that U = Y is a pivotal quantity.

c. Use the pivotal quantity from part (b) to find a a 85% lower confidence limit for .

d. Use the pivotal quantity from part (b) to find a a 85% upper confidence limit for .