Question

Let X and Y be random variables with E[X] = 3, E[Y] = -2, Var[X] = Var[Y] = 1, and Cov[X,Y] = -0.5. We also define W = 2X + Y + 3 and Z = X + Y - 2. Calculate Cov[W,Z].

Answer 1

To find Cov[W,Z], we need to calculate the covariance between W and Z using properties of variance and covariance.

Step-by-step explanation:

To calculate Cov[W,Z], we need to find the covariance between W and Z. First, let's find the variances of W and Z. We know that W = 2X + Y + 3, so Var[W] = Var[2X + Y + 3]. Since Var[X] = Var[Y] = 1, we can use the properties of variance to find Var[W]. Next, we need to find the covariance between W and Z. Cov[W,Z] = Cov[2X + Y + 3, X + Y - 2]. Again, we can use the properties of covariance to simplify this expression and calculate the covariance.