Question 3 Let X ERP and Ý ER4 be independent random vectors. Show that Cov(X,Y)= 0pxg.
Let X and Y be two independent random variables. Show that Cov (X, XY) = E(Y) Var(X).
Let X and Y be i.i.d. random variables with finite second moments. Show that Cov(X+Y, X ̶ Y) = 0.
1) Let X and Y be random variables. Show that Cov( X + Y, X-Y) Var(X)--Var(Y) without appealing to the general formulas for the covariance of the linear combinations of sets of random variables; use the basic identity Cov(Z1,22)-E[Z1Z2]- E[Z1 E[Z2, valid for any two random variables, and the properties of the expected value 2) Let X be the normal random variable with zero mean and standard deviation Let ?(t) be the distribution function of the standard normal random variable....
Problem 4 Let X be the following discrete random variable: Let Y = X2. Show that cov(X·Y) = 0, but X and Y are not independent random variable.
5. (2 points) Let X and Y be Bernoulli random variables. Show that X and Y are independent if and only if Cov(X, Y) = 0.
Let X, Y be random variables with f(x, y) = 1,-y < x < y, 0 < y < 1. Show that Cov(X,Y) = 0. Are X, Y independent?
Question # 7. Let X and Y be independent Normal random variables witht he same vari- ance. Show that X +Y and X-Y are independent. Question # 7. Let X and Y be independent Normal random variables witht he same vari- ance. Show that X +Y and X-Y are independent.
Let X and Y be two random variables such that: Var[X]=4 Cov[X,Y]=2 Compute the following covariance: Cov[3X,X+3Y]
How can I show the following? Let X, Y and Z be random variables on the same probability space such that Cov(X, Y ) < +∞. Show that Cov(X, Y ) = E(Cov(X, Y|Z)) + Cov (E (X|Z), E (Y|Z))
Let X be a standard normal distribution. Let ξ be another random variable, independent of X, which can take only two possible values, say -1 and 1. Moreover, assume that Ele] = 0. ( . (b) Find COV(x,Y). (c) Are X and Y independent? (d) Is the pair (X,Y) bivariate normal? a) Find the distribution of Y -£X Let X be a standard normal distribution. Let ξ be another random variable, independent of X, which can take only two possible...