[Q2] The joint density function of two continuous random variables X and Y is: f(x, y) = {cx²e/3 1 1.2).

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Chapter1: Combinatorial Analysis
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[Q2] The joint density function of two continuous random variables X and Y is:
Scx?e-y/3
1 < x < 6, 2 < y< 4
otherwise
(a) Determine the value of the constant c.
(b) Find the marginal distribution functions of X.
(c) Calculate P(X < 2.5, Y > 1.2).
(d) Draw the integration boundaries and write the integration only for P(X + Y < 6).
Transcribed Image Text:[Q2] The joint density function of two continuous random variables X and Y is: Scx?e-y/3 1 < x < 6, 2 < y< 4 otherwise (a) Determine the value of the constant c. (b) Find the marginal distribution functions of X. (c) Calculate P(X < 2.5, Y > 1.2). (d) Draw the integration boundaries and write the integration only for P(X + Y < 6).
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