Suppose that EX-EY-0, var(X) = var(Y) = 1, and corr(X,Y) = 0.5. (i) Compute E3X -2Y];...
1. Suppose E[X]-2 and E Y]-1. Evaluate the followings: a) E3X ] b) EX 2Y] c)
Assume X, Y are independent with EX = 1 EY = 2 Var(X) = 22 Var(Y) = 32 Let U = 2X + Y and V = 2X – Y. (a) Find E(U) and E(V). (b) Find Var(U) and Var(V). (c) Find Cov(U,V).
Suppose that f (x II 2y), 0 < x < 1,0 < y < 1. Find EX + Y).
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.
Suppose Var[X]=4, Var[Y]=1,and Cov [X,Y]= -1 . calculate Var [X-2Y+10]
(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).
Suppose that f(x,y) = (x + 2y), 0 SX S1, 0 Sy S 1. Find Var(X + Y).
Given Var(X) = 4, Var(Y) = 1, and Var(X+2Y) = 10, What is Var(2X-Y-3)? I know the answer is 15, I'm particularly interested in the specific steps involved with finding the cov(X,Y) in this problem. Please explain in detail, step by step how you come to cov(X,Y) = 0.5 in this equation. Please include any formulas you would need to use to find the cov(X,Y) in this equation.
9. Suppose Var(X] = 4, Var[Y-1, and Cov(X, Y] =-1. Calculate VarX-2Y + 101.
1. Suppose (x, Y) has bivariate normal distribution, E(x) E(Y)- 0, Var(X) σ , Var(Y) σ and Correl(X, Y) p. Calculate the conditional expectation E(X2|Y).