Assume X, Y are independent with EX = 1 EY = 2 Var(X) = 22 Var(Y)...
(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).
1. Suppose that E(X) E(Y) E(Z) 2 Y and Z are independent, Cov(X, Y) V(X) V(Z) 4, V(Y) = 3 Let U X 3Y +Z and W = 2X + Y + Z 1, and Cov(X, Z) = -1 Compute E(U) and V (U) b. Compute Cov(U, W). а.
Suppose XX and YY are independent random variables for which Var(X)=7Var(X)=7 and Var(Y)=7.Var(Y)=7. (a) Find Var(X−Y+1).Var(X−Y+1). (b) Find Var(2X−3Y)Var(2X−3Y) (c) Let W=2X−3Y.W=2X−3Y. Find the standard deviaton of W.W.
Suppose that EX-EY-0, var(X) = var(Y) = 1, and corr(X,Y) = 0.5. (i) Compute E3X -2Y]; and (ii) var(3X - 2Y) (ii) Compute E[X2]
4. Assume X ~ Uniform(0, 1) and let Y = 2X+1 and Z = X2 + 1. (a) Find Cov(X,Y), Var(X+Y), Var(X - Y) and Corr(X,Y). (b) Find Cov(X, Z), Var(X + Z), Var(X – Z) and Corr(X, Z).
4. (From Final 2015) Suppose that X =wage income, and U-nonwage income, and suppose 5, Var(X) 185, Var(U) that (X, U) are bivariate normal with EX)30, E(U) 35, and Cov(X,U)= 15. Suppose total income is in thousands of dollars. Y X +U. All variables are measured (b) What EY? State the joint distribution of (X, Y) 4. (From Final 2015) Suppose that X =wage income, and U-nonwage income, and suppose 5, Var(X) 185, Var(U) that (X, U) are bivariate normal...
X and z are independent. Var(x)=1 ; Var(z) = sigma ^2. E(z)= 0 and y= ax+b+z I) cov(x,y)= ? ii) corr(x,y)=? dependent Varvane 2.
Exercise 2 (2). Let X and ε be independent normally distributed random variables such that X∼N(5,4)andε∼N(0,9).LetY bearandomvariablegivenbyY =1+2X+ε.Compute: (a) E(Y ) (b) Var(Y ) (c) Cov(X, Y ) (d) Corr(X, Y ) (e) What is the value of the ratio Cov(X, Y )/Var(X) ? (f) If Y = 1 + 3X + ε instead, what would be the value of Cov(X, Y )/Var(X) ? (g) If Y = 1 + 7X + ε instead, what would be the value of...
9. Let X and Y be independent and identically distributed random variables with mean u and variance o. Find the following: (a) E[(x + 2)] (b) Var(3x + 4) (c) E[(X-Y)] (d) Cov{(X + Y), (X - Y)}
20. For X let E(X)-0 and sd(x)-2, and for Y let E(Y)--1 and sd(Y)-4. Find: (a) E(X-Y) and E (X Y). (b) Var(X- Y) and Var(X+ Y) if X and Y are independent. (c) EGX+ 흘 Y) and Var(1X+] Y) İf X and Y are independent. (d) Repeat (b) if, instead of independence, Cov(X, Y)- 1. soY is VarY larger