Question

Suppose you work at a banana factory, which operates as follows. There is a conveyor belt along which bananas are always coming your way. Each banana is rotten w.p. .07, and fresh w.p. .93, independent of all else. The first time that you get a banana which is rotten, you have to shut down the plant operations for the day. Up until that time, you process the fresh bananas you receive as follows. There is a “for-profit” crate, which can hold 333 bananas. The first 333 fresh bananas you process (if you even process that many fresh bananas before a rotten banana comes) must be packed into the for-profit crate. All remaining fresh bananas (again, before a rotten banana comes) are given to charity. Express the number of bananas given to charity C as a function of an appropriate r.v.

Answer 1

Solution

If the number of fresh bananas processed before a rotten banana comes is 333 or more, 333 bananas would be packed into the for-profit crate and the remaining bananas are given for charity.

If the number of fresh bananas processed before a rotten banana comes is less than 333, no banana can be packed into the for-profit crate and hence all bananas must be given for charity. Thus, if we define a random variable X as the number of fresh bananas processed before a rotten banana comes, then the number of bananas C given to charity is:

C = X – 333 if X ≥ 333

    = X if X < 333

Answer

DONE