

7. Suppose that Y = (y, ½, ½)T are jointly normally distributed with 2.0 1.0 0.5 μ = ElY]=| 2 | ,...
5. Suppose X is a normally distributed random variable with mean μ and variance 2. Consider a new random variable, W=2X + 3. i. What is E(W)? ii. What is Var(W)? 6. Suppose the random variables X and Y are jointly distributed. Define a new random variable, W=2X+3Y. i. What is Var(W)? ii. What is Var(W) if X and Y are independent?
Suppose that X, Y, and Zare jointly distributed random variables, that is, they are defined on the same sample space. Suppose that we also have the following. E(x)-4 E(Y) 2 E(Z)-7 Var (x) -28 Var(Y)-3 Var (Z) -44 Compute the values of the expressions below. E(Y -1) 5Z + 4X Var (4Y-3)
Suppose that X, Y, and Z are jointly distributed random variables, that is, they are defined on the same sample space. Suppose that we also have the following. E(x)-4 E(Y) 2 E(Z)-7 Var (x) -28 Var(Y)-3 Var (Z) -44 Compute the values of the expressions below. E(Y 1) 5Z + 4x Var (4Y-3)
Suppose that X, Y, and Z are jointly distributed random variables, that is, they are defined on the same sample space. Suppose that we also have the following. E(X)-8 E(Y)-7 E(Z)-2 Var (x) 24 Var (Y) 2 Var (z) 29 Compute the values of the expressions below. E (5x- 4) Var (-2 5z) - [D
Suppose that X, Y, and Zare jointly distributed random variables, that is, they are defined on the same sample space. Suppose that we also have the following. E(x)--8 Var(x)=24 E(r) = 7 Var (r) = 2 E(z) =-2 Var(Z)-29 Compute the values of the expressions below. E (5X-4) Var(-21, 52)=
Suppose that X, Y, and Z are jointly distributed random variables, that is, they are defined on the same sample space. Suppose that we also have the following. E(x) = 3 Var (x) = 19 E(r)--2 Var (r)-36 E(Z)-6 Var (Z)-45 Compute the values of the expressions below. E (2 1)
Suppose that X, Y, and Z are jointly distributed random variables, that is, they are defined on the same sample space. Suppose that we also have the following. ar (x) 34 Var (Y)- Var() 35 Compute the values of the expressions below. E 4 + 5Z2) -4Z-5x -О Var (-5Y+2)
Suppose that X, Y, and Z are jointly distributed random variables, that is, they are defined on the same sample space. Suppose that we also have the following. E(x)-3 E(Y)9 E(Z)-2 Var(X) = 36 par(r)=19 par(Z)-10 Compute the values of the expressions below E (32 +3) 5Y+ 2x Var (5-2)-
Suppose that X, Y, and Z are jointly distributed random variables, that is, they are defined on the same sample space. Suppose that we also have the following. E(x)-5 ECY)4 E(Z)--8 Var (x)-39 Var (Y)-11 Var (z) 37 Compute the values of the expressions below. E(2 -2z) 35 30 Var (sz)-5-D
Suppose that X, Y, and Z are jointly distributed random variables, that is, they are defined on the same sample space. Suppose that we also have the following. Var (r)-30 Var (r)-36 Var (z) 23 Compute the values of the expressions below 2X + 32 Var (Z-4)-