The number of defective components produced by a certain process in one day has a Poisson distribution with mean 20. Each defective component has probability 0.60 of being repairable.
a. Find the probability that exactly 15 defective components are produced.
b. Given that exactly 15 defective components are produced, find the probability that exactly 10 of them are repairable.
c. Let N be the number of defective components produced, and let X be the number of them that are repairable. Given the value of N, what is the distribution of X?
d. Find the probability that exactly 15 defective components are produced, with exactly 10 of them being repairable.
(a) Let N be the number of defective components produced. Then N ~ Poisson(20).
(b) Let X be the number that are repairable. Then X ~ Bin(15,0.6).
(c) Given N,X ~ Bin(N, 0.6).
(d)Let N be the number of defective components, and let X be the number that are repairable.
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