remember that1.) Let X have an exponential dist. with mean, theta > 0. Show that
P(X > x + y | X > x) = P(X > y)
P(X>a) =1-F(a) where F is the cdf of X.
This is where to start. By the sound of it I think you will be able to continue nicely.
Start by finding the distribution function of Y. Then note that the function W(Y) is strictly increasing. Can you continue?2.) Let Y have a uniform dist. U (0, 1)
and let W=a +(b-a)Y a<b
a) Find the dist. function of W. [Hint: find P[a+ (b-a)Y < or =w]
b) How is W distributed?