Let X denote the number of Canon SLR cameras sold during a particular week by a

Question

Let X denote the number of Canon SLR cameras sold during a particular week by a certain store. The pmf of X is Sixty-five percent of all customers who purchase these cameras also buy an extended warranty. Let Y denote the number of purchasers during this week who buy an extended warranty. (a) What is P(X = 4, Y = 2)? (Round your answer to four decimal places.) (b) Calculate P(X = Y). (Round your answer to four decimal places.) (c) Determine the joint pmf of X and Y. (y x)(0.65)^y (0.65)^x - y middot p_X(x) (x y)(0.65)^y (0.35)^x - y middot p_X(x) (x y)(0.65)^x (0.35)^x - y middot p_X(x) (y x)(0.65)^x (0.65)^x - y middot p_X(x) Determine the marginal pm of Y. (Round your answers to four decimal places.)

Explanation / Answer

I think you want marginal pmf of Y part only:

here from binomial distribution of Y and x;S jOINT probabilty distribution:

hence marginal pmf of Y is:

X Y 0 1 2 3 4 Total 0 0.1 0.07 0.03675 0.010719 0.002251 0.2197 1 0 0.13 0.1365 0.059719 0.016721 0.3429 2 0 0 0.12675 0.110906 0.046581 0.2842 3 0 0 0 0.068656 0.057671 0.1263 4 0 0 0 0 0.026776 0.0268 Total 0.1 0.2 0.3 0.25 0.15 1

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