Question: 10. In the sample space in exercise 9, define Y P3 j1 jnj , and consider the pair of random variables X;Y. (a) Determine

10. In the sample space in exercise 9, define Y ¼

P3 j¼1 jnj , 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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