# Question

There are two possible causes for a breakdown of a machine. To check the first possibility would cost C1 dollars, and, if that were the cause of the breakdown, the trouble could be repaired at a cost of R1 dollars. Similarly, there are costs C2 and R2 associated with the second possibility. Let p and 1 − p denote, respectively, the probabilities that the breakdown is caused by the first and second possibilities. Under what conditions on p, Ci, Ri, i = 1, 2, should we check the first possible cause of breakdown and then the second, as opposed to reversing the checking order, so as to minimize the expected cost involved in returning the machine to working order?

If the first check is negative, we must still check the other possibility.

If the first check is negative, we must still check the other possibility.

## Answer to relevant Questions

A person tosses a fair coin until a tail appears for the first time. If the tail appears on the nth flip, the person wins 2n dollars. Let X denote the player’s winnings. Show that E[X] = +∞. This problem is known as the ...Find Var(X) and Var(Y) for X and Y as given in Problem 21. Problem 21 Four buses carrying 148 students from the same school arrive at a football stadium. The buses carry, respectively, 40, 33, 25, and 50 students. One of the ...It is known that diskettes produced by a certain company will be defective with probability .01, independently of each other. The company sells the diskettes in packages of size 10 and offers a money-back guarantee that at ...If you buy a lottery ticket in 50 lotteries, in each of which your chance of winning a prize is 1/100, what is the (approximate) probability that you will win a prize (a) At least once? (b) Exactly once? (c) At least twice? Suppose in Problem 72 that the two teams are evenly matched and each has probability 12 of winning each game. Find the expected number of games played. Problem 72 Two athletic teams play a series of games; the first team to ...Post your question

0