Suppose that Cov(X,Y ) = 0.9 and Cov(X,Z) = −0.7.
(a) What is Cov(X,Y + Z)?
b) What is Cov(3X,−2Y )?
Suppose that Cov(X,Y ) = 0.9 and Cov(X,Z) = −0.7. (a) What is Cov(X,Y + Z)?...
X,Y, and Z are random variables. Var(X) = 2, Var(Y) = 1, Var(Z) = 5, Cov(X,Y) = 3, Cov(X, Z) = -2, Cov(Y,Z) = 7. Determine Var(3X – 2Y - 2+10)
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.
Var(Y) =y Var(X)=x Cov(X,Y) =z What is Cov(XY,XY)
Let X and Y have the following joint distribution X/Y 0 1 0 0.4 0.1 1 0.1 0.1 2 0.1 0.2 a) Find Cov(4+2X, 3-2Y) b) Let Z = 3X-2Y+2 Find E[Z] and σ 2Z c) Calculate the correlation coefficient between X and Y. What does this suggest about the relationship between X and Y? d) Show that for two nonzero constants a and b Cov(X+a, Y+b) = Cov(X,Y)
Suppose Var[X]=4, Var[Y]=1,and Cov [X,Y]= -1 . calculate Var [X-2Y+10]
9) Compute T30T20T1(x, y) for T1 (x,y)=(-2y,3x,x-2y) T2(x,y,z)=(y,z,x) T3(x,y,z)=(x +z,y-z)
9. Suppose Var(X] = 4, Var[Y-1, and Cov(X, Y] =-1. Calculate VarX-2Y + 101.
10. Suppose Var|X] -2, VarlY] - 2, Var[Z]1, CovlX, Y10, CovlX, Z and Cov[Y, Z] =-1. Calculate Var(X + Y-2Z + 5.
1. Suppose the joint density of X and Y is given by f(x,y) = 6e-3x-2y, if 0 < x < inf., 0 < y < inf, 0 elsewhere. Part A, Find P( X < 2Y) Part B, Find Cov(X,Y) Part C, Suppose X and Y have joint density given by f(x,y) = 24xy, when 0<= x <=1, 0 <= y <=1, 0 <= x+y <=1, and 0 elsewhere. Are X and Y independent or dependent random variables? why?
10.3.8 Suppose that Y = E(Y | X) + Z, where X, Y and Z are random variables. (a) Show that E (Z | X) = 0. (b) Show that Cov(E(Y | X), Ζ) = 0. (Hint. Write Z-Y-E(YİX) and use Theo- rems 3.5.2 and 3.5.4.) (c) Suppose that Z is independent of X. Show that this implies that the conditional distribution of Y given X depends on X only through its conditional mean. (Hint: Evaluate the conditional distribution function...