Question: Q1.The joint probability density function of a bivariate variable (X, Y) is given by f xy (x, y) ={k (x + y) ; 0 <

Q1.The joint probability density function of a bivariate variable (X, Y) is given by

fxy (x, y) ={k (x + y) ; 0 < x < 3 , 0 < y < 3

where k is constant.

(i) Find the value of k.

(ii) Find the marginal probability density function of X and Y.

(iii) Are X and Y independent?

Q2.The joint probability density function of a bivariate variable (X, Y) is given by

fxy (x, y) ={k ( 2 x + y) ; 0 < x < 1 , 0 < y < 1 where k is constant.

(i) Find the value of k.

(ii) Find the marginal probability density function of X and Y.

(iii)Conditional density of X for given Y and use it to evaluate P (X<=1/2 / Y=1).

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