An aircraft maintenance facility specializes in detailed checkups of 4 older gen

Question

An aircraft maintenance facility specializes in detailed checkups of 4 older generation jet engines and 3 new jet engines that went into operation this year. In the next 6-months the independent probability that each of the 4 older jet engines will require check ups is .15 while the same independent probability for each of the 3 new jet engines is 0.07. Let X be the total number of jet engines ie the sum of old and new engines, that are checked by the maintained facility in a six month period.

a) Is X binomially distributed random variable? Why?

b) What is the probability that exactly 5 engines will need to be check by the facility in the next 6 months? In other words, what is probability P(X=5)?

Explanation / Answer

a) No, X is not binomially distributed random variable.

Reason :

Suppose that Uand V are independent random variables, and that U has the binomial distribution with parameters m and p, and V has the binomial distribution with parameters n and p. Then U+V has the binomial distribution with parameters m+n and p.

In this case the value of p are different i.e 0.15 and 0.07

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