(Solved): 5.102 A firm purchases two types of industrial chemicals. Type I chemical costs $3 per gallon, where ...

5.102 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, Y_(1), are 40 and 4 , respectively. The amount of type II chemical purchased, Y_(2), has E(Y_(2))=65 gallons and V(Y_(2))=8. Assume that Y_(1) and Y_(2) are independent and find the mean and variance of the total amount of money spent per week on the two chemicals.