Question: Problem 2 [25 marks] An urn contains 5 red balls, 6 green balls and 3 blue balls. A total of 3 balls are selected without

Problem 2 [25 marks]

An urn contains 5 red balls, 6 green balls and 3 blue balls. A total of 3 balls are selected without replacement from the urn. Denote X1 the number of red balls selected and X2 the number of green balls selected.

1

(a) Find the joint probability mass function of X1 and X2, p(x1,x2). [5 marks] (b) Find the marginal probability mass functions of X1 and X2, p1(x1) and p2(x2). [5 marks]

(c) Compute the correlation between X1 and X2. [15 marks]

Problem 2 [25 marks]An urn contains 5 red balls, 6 green ballsand 3 blue balls. A total of 3 balls are selected without

Problem 2 [25 marks] An urn contains 5 red balls, 6 green balls and 3 blue balls. A total of 3 balls are selected Without replacement from the urn. Denote X1 the number of red balls selected and X2 the number of green balls selected. (a) Find the joint probability mass function of X1 and X2, p(:1:1,:1:2). [5 marks] (b) Find the marginal probability mass functions of X1 and X2, 191(331) and p2(a:2). [5 marks] ((3) Compute the correlation between X1 and X2. [15 marks]

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