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]
Let X and Y be two random variables such that: Var[X]=4 Cov[X,Y]=2 Compute the following covariance:...
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...
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....
X,Y, and Z are random variables. Var(X) = 2, Var(Y) = 1, Var(Z) = 5, Cov(X,Y) = 3, Cov(X, Z) = -2, Cov(Y,Z) = 7. Determine Var(3X – 2Y - 2+10)
4. Recall that the covariance of random variables X, and Y is defined by Cov(X,Y) = E(X - Ex)(Y - EY) (a) (2pt) TRUE or FALSE (circle one). E(XY) 0 implies Cov(X, Y) = 0. (b) (4 pt) a, b, c, d are constants. Mark each correct statement ( ) Cov(aX, cY) = ac Cov(X, Y) ( ) Cor(aX + b, cY + d) = ac Cov(X, Y) + bc Cov(X, Y) + da Cov(X, Y) + bd ( )...
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)?
(2. Assume that X, Y, and Z are random variables, with EX) = 2, Var(X) = 4, E(Y) = -1, Var(Y) = 6, E(Z) = 4, Var(Z) = 8,Cov(X,Y) = 1, Cov(X, Z) = -1, Cov(Y,Z) = 0 Find E(3X + 4y - 62) and Var(3x + 4y - 62).
6. (a) State the definition of the covariance Cov(x,Y) of two random variables X and Y. (b) Consider the two continuous random variables X and Y of Ques- tion 2. with joint density f(x, y) otherwise i. Find μχ.y the expectations of X, Y respectively.
Let X and Y be two independent random variables. Show that Cov (X, XY) = E(Y) Var(X).
6 Suppose that X and Y are random variables such that Var(X) Var(Y)-2 and Cov(x,y)- 1. Find the value of Var(3.X-Y+2)
2. Properties of Correlation and Covariance: Two random variables Y and Z are represented by the following relationships Y = 0.5+0.6X Z = 0.2+0.3x where X is another random variable. You can treat the variance, Var(X), as a given constant. It may help to give Var(X) a name, ie. Var(x)ox2 a. Calcuate var(Y) and Var(Z) as a function of Var(X). Which is hrger? b. Calcuate Cov(Y,Z), Cov(X,Z) and Cov(X,Y) as a function of var(X). c. Calcuate Corr(Y,Z), Corr(X,Z) and Corn(X,Y)...