A batch of 100 motors has been manufactured and andy and

Reference no: EM13617841

1. A batch of 100 motors has been manufactured, and Andy and Bob are applying a standard stress test to them. Andy is assigned 40 motors to test, and Bob is assigned the remaining 60 motors to test. Each motor has probability p of failing; assume the motors and tests are independent. Let X be the number of failures among Andy's motors, Y be the number of failures among Bob's motors, and let T = X + Y.

A. Calculate the conditional probability P(X = x|T = t).

B. Can you identify this probability distribution?

C. Find expressions for E(X|T) and V ar(X|T), as functions of T.

2. Suppose the probability that it rains on any given day is 20%, and that days are independent. On any rainy day, the amount of rainfall follows an Expo(2) distribution. Calculate the mean and variance of the total rainfall during a 30-day month.

Reference no: EM13617841

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