32 In the sample space in exercise 31, define Y n1, and consider the pair of random variables X Y (a) Determine the range of X Y and associated p d f f x y (b) Calculate the marginal p d f s f x and f y (c) Calculate the conditional p d f s f x j y and f y j x, and confirm the law of total probabil...

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32. In the sample space in exercise 31, define Y n1, and consider the pair of...

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32. In the sample space in exercise 31, define Y ¼ n1, and consider the pair of random variables ðX;YÞ.

(a) Determine the range of ðX;YÞ and associated p.d.f. f ðx; yÞ.

(b) Calculate the marginal p.d.f.s f ðxÞ and f ðyÞ.

(c) Calculate the conditional p.d.f.s f ðx j yÞ and f ðy j xÞ, and confirm the law of total probability, that f ðxÞ ¼

P y f ðx j yÞ f ðyÞ and f ðyÞ ¼

P x f ðy j xÞ f ðxÞ.

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