Please do by hand. Thanks in advance.
Please do by hand. Thanks in advance. 1. Let X and Y be random variables with...
Please do by hand. Thanks in advance. 2. Let X and Y be two random variables. If Var(X) = 4, Var(Y) = 16, and Cov(X,Y) = 2, then what is Var(3Y - 2x)?
Please do by hand. Thanks in advance. 8. Let X and Y be random variables with a bivariate normal distribution with parameters • px = 5 • Ox= 3 • My = 3 • Oy = 2 • p=.4 a) Find the expected value and variance of Z=4X-Y. b) Find the covariance of X and Z. c) Identify the distribution of Y. d) Identify the distribution of Y|X = 5.
9. Let X and Y be two random variables. Suppose that σ = 4, and σ -9. If we know that the two random variables Z-2X?Y and W = X + Y are independent, find Cov(X, Y) and ρ(X,Y). 10. Let X and Y be bivariate normal random variables with parameters μェー0, σ, 1,Hy- 1, ơv = 2, and ρ = _ .5. Find P(X + 2Y < 3) . Find Cov(X-Y, X + 2Y) 11. Let X and Y...
Please do by hand. Thanks in advance. b and c below are a part of the problem. 3. Let Xi and X2 be independent random variable, each following an exponential(1) distribution. Define new random variables Y = X1 - X, and Y2 = X1 + X2. a) Find the joint pdf of Y and Y2. b) Find the marginal pdf of Yı c) Find the marginal pdf of Y2
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....
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]
Example of Covariance II 4 points possible (graded) Let X, Y be random variables such that • X takes the values +1 each with probability 0.5 . (Conditioned on X) Y is chosen uniformly from the set {-3X - 1,-3x, -3x+1}. (Round all answers to 2 decimal places.) What is Cov(x,x) (equivalent to Var (X))? Cov(X, X) = What is Cov(Y,Y) (equivalent to Var (Y))? Cov(Y,Y)= What is Cov(X,Y)? Cov(X,Y)= What is Cov(Y,X)? Cov(Y,X)= Submit You have used 0 of...
9. Let X and Y be independent and identically distributed random variables with mean u and variance o. Find the following: (a) E[(x + 2)] (b) Var(3x + 4) (c) E[(X-Y)] (d) Cov{(X + Y), (X - Y)}
Let X and Y be two independent random variables. Show that Cov (X, XY) = E(Y) Var(X).
2. Let X and Y be two random variables with a joint distribution (discrete or continuous). Prove that Cov(X,Y)= E(XY) - E(X)E(Y). (15 points) 3. Explain in detail how we can derive the formula Var(X) = E(X) - * from the formula in Problem 2 above. (Please do not use any other method of proof.) (10 points)