# Functions of Random Variables - The method of distribution functions

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).

https://brainmass.com/statistics/probability-density-function/functions-random-variables-distribution-functions-16878

#### Solution Summary

Density functions are found in the solution. The solution is detailed and well presented.