The discrete random variables ? and ? have joint probability function ?, where ? is given...

Question

Question

The discrete random variables ? and ? have joint probability function ?, where ? is given by the following table:

a) Determine ?(1 < ? ≤ 3, 1 ≤ ? ≤ 2). [4 marks]

b) Calculate ?(?^2 ?). [4 marks]

c) Find the marginal probability functions ? and ℎ of ? and ? respectively. [4 marks]

d) Are ? and ? independent? Give reasons to support your answer. [2 marks]

e) Determine the joint distribution function of ? and ?. [4 marks]

Answer 1

Answer #1

+ 48) +0 x(8 + 3) = 」3.85 се 0.25 if ㅈ23 o 33 (d) PTxh] x P[γ«W=o.us x0.45 0.0475

Answer 2

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