The probability distribution of the discrete random variable X is: f(X) = k2³-x , for x = 4,5, 6, 7 %3D ) Find.

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Chapter1: Combinatorial Analysis
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[Q1] The probability distribution of the discrete random variable X is:
f (X) = k2³-x , for x = 4,5, 6, 7
%3D
(а) Find:
• the value of the constant k.
• The mean E(X).
• The variance Var(X).
(b) Sketch F(X).
[Q2] The joint density function of two continuous random variables X and Y is:
f(x, y) = {cx'e-/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:[Q1] The probability distribution of the discrete random variable X is: f (X) = k2³-x , for x = 4,5, 6, 7 %3D (а) Find: • the value of the constant k. • The mean E(X). • The variance Var(X). (b) Sketch F(X). [Q2] The joint density function of two continuous random variables X and Y is: f(x, y) = {cx'e-/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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