Expected value based on Binomial and Geometric distribution.
A certain exterminator specializes in Apexis rodents. Apexis rodents ALWAYS infest the basement of a house. They sometimes, but not always, infest the rooms of the house. When the exterminator looks for the Apexis nest in the basement he has a 10 percent chance, every minute, of finding it. There is a 40% chance that any given room of the house is infested. Let Y be the number of minutes spent searching the basement for the Apexis rodents. Let X is the number of rooms in a six room house infested by Apexis rodents. The exterminator's statistician assures him that X and Y are independent
a. What is the distribution of X? Declare its mean and variance.
b. What is the distribution of Y? State its mean and variance.
c. The exterminator charges a hefty fifty dollars for every minute spent searching the basement. However he feels bad when the infestation goes beyond the basement and refunds 5 dollars for every room that is infested. Let C be the amount charged to an infested house. Find the expected value and variance of C.
d. Find out E (XY)