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Functions of Random Variables - The method of distribution functions

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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).

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Solution Summary

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

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