UCS410 Thapar Institute of Engineering and Technology (TIET) Solution

Probability and Statistics(UCS410) Exp. sheet 06 (Joint probability mass and density functions)
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(1) The joint probability density of two random variables X and Y is

 2(2x + 3y)/5;
f(x,y) =
 0; 0 ≤ x,y ≤ 1
elsewhere
Then write a R-code to
(i) check that it is a joint density function or not? (Use integral2()) (ii) find marginal distribution g(x) at x = 1.
(iii) find the marginal distribution h(y) at y = 0.
(iv) find the expected value of g(x,y) = xy.
(2) The joint probability mass function of two random variables X and Y is
f(x,y) = {(x + y)/30; x = 0,1,2,3; y = 0,1,2}
Then write a R-code to
(i) display the joint mass function in rectangular (matrix) form.
(ii) check that it is joint mass function or not? (use: Sum())
(iii) find the marginal distribution g(x) for x = 0,1,2,3. (Use:apply())
(iv) find the marginal distribution h(y) for y = 0,1,2. (Use:apply()) (v) find the conditional probability at x = 0 given y = 1.
(vi) find E(x),E(y),E(xy),V ar(x),V ar(y),Cov(x,y) and its correlation coefficient.