Let Y be a random variable with probability density function

Let Y be a random variable with probability density function given by f(y)= 2(1-y) for 0<y<1 and 0 elsewhere

a. find the density function of U1=2Y-1

b. Find the density function of U2=1-2Y

c. find the density function of U3=Y^2

d. find E(U1), E(U2), E(U3)

Solution

a)

U1 = 4 (1-y) - 1

b)

U2 = 1 - 4(1-y)

c)

U3 = [2(1-y)]^2

d)

I can gladly help you but you should post it in a new question