# Question

Determine whether or not each of the following pairs of random variables are independent:

(a) The random variables described in Exercise 5.6;

(b) The random variables described in Exercise 5.7;

(c) The random variables described in Exercise 5.14;

(d) The random variables described in Exercise 5.13.

(a) The random variables described in Exercise 5.6;

(b) The random variables described in Exercise 5.7;

(c) The random variables described in Exercise 5.14;

(d) The random variables described in Exercise 5.13.

## Answer to relevant Questions

Consider two discrete random variables X and Y which take on values from the set {1, 2, 3, ….,K}. Suppose we construct an n ˟ n matrix ρ whose elements comprise the joint PMF of the two random variables. That is, if is ...Two random variables have a joint Gaussian PDF given by (a) Identify σ2x, σ2y, and ρX, Y. (b) Find the marginal PDFs, f X (x) and f Y (y). (c) Find the conditional PDFs, f X| Y (x| y) and f Y| X (y| x) a) Find the joint PGF for the pair of discrete random variables given in Exercise 5.13. b) From the result of part (a), find E [M] and E [N]. c) From the result of part (a), find E [MN]. In Exercise 5.13 Let and be jointly Gaussian random variables with E [X] = 1, E [Y] = –2, Var (X) = 4, Var (Y) = 9, and ρX, Y. Find the PDF of Z = 2X – 3Y – 5. For positive constants and, a pair of random variables has a joint PDF specified by . Fx, y (x, y) = abe-(ax = by) u (x) u (y) (a) Find the joint CDF, Fx, y (x, y). (b) Find the marginal PDFs, fx (x) and fy (y). (c) Find ...Post your question

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