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A firm purchases two types of industrial chemicals. Type I
Chapter 5, Problem 102E(choose chapter or problem)
Problem 102E
A firm purchases two types of industrial chemicals. Type I chemical costs $3 per gallon, whereas type II costs $5 per gallon. The mean and variance for the number of gallons of type I chemical purchased, Y1, are 40 and 4, respectively. The amount of type II chemical purchased, Y2, has E(Y2) = 65 gallons and V (Y2) = 8. Assume that Y1 and Y2 are independent and find the mean and variance of the total amount of money spent per week on the two chemicals.
Questions & Answers
QUESTION:
Problem 102E
A firm purchases two types of industrial chemicals. Type I chemical costs $3 per gallon, whereas type II costs $5 per gallon. The mean and variance for the number of gallons of type I chemical purchased, Y1, are 40 and 4, respectively. The amount of type II chemical purchased, Y2, has E(Y2) = 65 gallons and V (Y2) = 8. Assume that Y1 and Y2 are independent and find the mean and variance of the total amount of money spent per week on the two chemicals.
ANSWER:
Solution:
Step 1 of 2:
We have two types 0f industrial chemicals. Type 1 chemical costs $3 per gallon and Type 2 costs $5 per gallon.
We have, E() = 40, V(
) = 4, E(
) = 64, and V(
) = 8
The total amount spent is the sum of products of the costs and the number of gallons
S = 3+ 5
The claim is to find the mean and variance