Solution Found!
In Exercise 6.4, we considered a random variable Y that
Chapter 6, Problem 24E(choose chapter or problem)
Problem 24E
In Exercise 6.4, we considered a random variable Y that possessed an exponential distribution with mean 4 and used the method of distribution functions to derive the density function for U = 3Y + 1. Use the method of transformations to derive the density function for U .
Reference
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 .
b Use the answer in part (a) to find E(U ).
Questions & Answers
QUESTION:
Problem 24E
In Exercise 6.4, we considered a random variable Y that possessed an exponential distribution with mean 4 and used the method of distribution functions to derive the density function for U = 3Y + 1. Use the method of transformations to derive the density function for U .
Reference
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 .
b Use the answer in part (a) to find E(U ).
ANSWER:
Step 1 of 2
a)The probability density function for U is expressed as:
FU(u) = Pr(U ? u) = Pr(3Y+1 ? u)
By transforming the random variable, we have:
Y ? (u-1) / 3
Therefore, the probability density function for U is:
fU(u) = fY((u-1) / 3) * (3 / (1/4)) = 12fY((u-1) / 3) = 12e^-((u-1) / 3) / 4