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  3. assume that the random variables x and y have the...

Question: assume that the random variables x and y have the...

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CHAPTER A. CONDITIONAL X -1 0 1/36 1/6 1/12 0 1/18 0 1/18 0 1 0 1/36 1/6 1/12 2 N/12 0 1/12 1/6 Table 1.6: Joint, distribution.

Assume that the random variables X and Y have the joint distribution given in Table 4.6.

(a) What is P ( X ≥ 1 and Y ≤ 0)?

(b) What is the conditional probability that Y ≤ 0 given that X = 2?

(c) Are X and Y independent?

(d) What is the distribution of Z = XY ?

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