# Question: Let and be random variables with means x and y

Let and be random variables with means μx and μy, variances σ2x and σ2y, and correlation coefficient ρ X, Y.

(a) Find the value of the constant which minimizes.

(b) Find the value of when is given as determined in part (a).

(a) Find the value of the constant which minimizes.

(b) Find the value of when is given as determined in part (a).

## Relevant Questions

For the discrete random variables whose joint PMF is described by the table in Exercise 5.14, compute the following quantities: (a) E [XY]; (b) Cov (X, Y); (c) ρ X,Y; (d) E [Y| X]. 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 ...Two random variables have a joint Gaussian PDF given by Find E [X], E [Y], Var (X), VAr (Y), ρ X,Y, Cov (X,Y), and E[XY]. The joint moment- generating function (MGF) for two random variables, and , is defined as Develop an equation to find the mixed moment E [Xn Ym] from the joint MGF. Let and be independent and both uniformly distributed over (0, 2π. Find the PDF of Z = (X + Y) mod 2π.Post your question