Probability

Variance

Covariance - Properties

         

If the covariances between random variables X, X, Y, Y, W, W, and Z Z are as follows: Cov(X,Y)=0.3Cov(X,W)=0.2Cov(X,Z)=0Cov(Y,W)=0.8Cov(Y,Z)=0Cov(W,Z)=0.4, \begin{matrix} \text{Cov}(X,Y) = 0.3& \text{Cov}(X,W) = 0.2 \\ \text{Cov}(X,Z) = 0 & \text{Cov}(Y,W) = 0.8 \\ \text{Cov}(Y,Z) = 0 & \text{Cov}(W,Z) = 0.4, \end{matrix} what is the covariance between 3X+2W 3X+2W and 8Y+4Z? 8Y + 4Z?

If random variables X X and Y Y have the following variance and covariance: Var(X)=6,Var(Y)=8,Cov(X,Y)=1, \text{Var}(X) = 6, \text{Var}(Y) = 8, \text{Cov}(X,Y) = 1, what is Var(6X+8Y) \text{Var}( 6X + 8Y ) ?

If the covariance between random variables X X and Y Y is Cov(X,Y)=0.3, \text{Cov} (X,Y) = 0.3, what is Cov(4X,2Y)? \text{Cov} ( 4X , 2Y )?

If the covariance between random variables X X and Y Y is Cov(X,Y)=0.2, \text{Cov} (X,Y) = 0.2, what is Cov(X+6,Y+2)? \text{Cov} ( X + 6 , Y + 2 )?

Let X X be a random variable uniformly distributed in the domain [1,1], [-1,1], and let Y=X2. Y = X^2. What is the covariance between X X and Y? Y?

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