See the attached file.
1) Let Y be a random variable with a density function given by
f(y1) = 3/2y^2 , -1 <y1<1
f(y1) = 0, elsewhere
a) find the density function of U1 = 3Y using the method of distribution.
b) find the density function of U2 = 3-Y using the method of distribution.
c) find the density function of U3 = 3y^2 using the method of distribution.
2) The amount of flour used per day by a bakery is a random variable Y that has an exponential distribution with mean equal to 4 tons. The cost of the flour is proportional to U=3Y+1
a) Find the probability density function for U. (using method of distribution)
b) Use the answer in a) to find E(U).
Density functions are found in the solution. The solution is detailed and well presented.