The joint pmf of X and Y is given in the following table. y P(x.v) 1 0.02 0.06 0.03 2 0.07 0.15 0.20 0.08 0.25 0.14 Compute a. The covariance for X and Y b. p for X and Y
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- Use the expected value properties to obtain the E[Y] of the following system : y = 3x + 1 , where E[X] =3For any continuous random variables X, Y , Z and any constants a, b, show the following from the definition of the covariance:Let X have a mean of 13 and a variance of 1.1. Let Y have a mean of 9.1 and a variance of 0.75. The covariance of x and y is 0.35. Let Z=4X – 5Y+2. What is the mean and variance of Z?
- Assume that as a portfolio manager the beta of your portfolio is 1.15 and that your performance is exactly on target with the SML data under condition 1. If the true SML data is given by condition 2, how much does your performance differ from the true SML? (1) RFR = 0.0625 Rm(proxy) = 0.12 (2) RK = 0.078 Rm(true) = 0.10If the PDF of X is f(x)=2x/k2 for 0<x<k, for what value of k is the variance of X equal to 2?1. Find the population covariance between X and Y .2. Find E[Y |X = x].3. Find Var[Y |X = x].
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