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For the problem described in Exercise 8, let X denote the number of defective items produced by the machine and let Y denote the number of non-defective items produced by the machine. Show that X and Y are independent random variables.

Exercise 8

Suppose that the total number of items produced by a certain machine has a Poisson distribution with mean X; that all items are produced independently of one another; and that the probability that any given item produced by the machine will he defective is p. Determine the marginal distribution of the number of defective items produced by the machine.

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Category:- Statistics and Probability
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