13. Consider the random variables X and Y with the following expectations: E(X)= 2, E(Y)=1 E(X²)=15,...
Consider two random variables, X and Y. Let E(X) and E(Y) denote the population means of X and Y respectively. Further, let Var(X) and Var(Y) denote the population variances of X and Y. Consider another random variable that is a linear combination of X and Y Z- 3X- Y What is the population variance of Z? Assume that X and Y are independent, which is to say that their covariance is zero.
For the random variables X and Y having E(X) = 1, E(Y) = 2, Var (X) = 6, Var (Y) = 9, and Pxy = -2/3. Find a) The covariance of X and Y. b) The correlation of X and Y. c) E(X2) and E(Y2).
Suppose x and y are two random variables. If y= 3x -2 then the mathematical expectations and variances of x and y are related as follows E(y)=3E(x)-2, V(y)=9V(x)-2 E(y)=3E(x), V(y)=9V(x) E(y)=3E(x)+2, V(y)=9V(x)+2 E(y)=3E(x)-2, V(y)=9V(x)
Let X and Y be two random variables such that E(X) = 2, E(Y) = 5 and E(XY)=7. The covariance of (X, Y) is equal to: a. 17 b. 14 c. 3 d. -3 a O с Od
3. Let the random variables X and Y have the joint probability density function 0 y 1, 0 x < y fxy(x, y)y otherwise (a) Compute the joint expectation E(XY) (b) Compute the marginal expectations E(X) and E (Y) (c) Compute the covariance Cov(X, Y)
3. Let the random variables X and Y have the joint probability density function fxr (x, y) = 0 <y<1, 0<xsy otherwise (a) Compute the joint expectation E(XY). (b) Compute the marginal expectations E(X) and E(Y). (c) Compute the covariance Cov(X,Y).
please be clear and solved all Let X and Y be two Independent random variables such that V(X) =1 and V(Y) =2. Then V(3X-2Y+5) is equal: a. 25 b. 20 17 d. 15 C. O a d Let X and Y be two random variables such that E(X) = 2, E(Y) = 5 and E(XY)=7. The covariance of (X, Y) is equal to: a. 17 b. 14 c. 3 d. -3 a O с Od Question 3* 10 points Light...
2. Consider random variables X and Y with the following joint PDP: 2xyn (a) Suppose that U-In(XY) and V- In(X). Express X and Y in terms of U and V. (b) Use part (a) to find the Jacobian of the transformation from (X, Y) 'to (U, v) (c) Use (a) and (b) to show that the joint PDF of U and V is:
4. Suppose that X and Y are random variables with E(X) = 2, E(Y) = 1. E(X*) = 5, E(Y2-10, and E(XY) = 1 (a) Compute Corr(X,Y) (b) Choose a number c so that X and X +cY are uncorrelated
2) Two statistically-independent random variables, (X,Y), each have marginal probability density, N(0,1) (e.g., zero-mean, unit-variance Gaussian). Let V-3X-Y, Z = X-Y Find the covariance matrix of the vector, 2) Two statistically-independent random variables, (X,Y), each have marginal probability density, N(0,1) (e.g., zero-mean, unit-variance Gaussian). Let V-3X-Y, Z = X-Y Find the covariance matrix of the vector,