Question: Let X, Y, and Z be jointly distributed random variables. Prove that Cov(X + Y, Z) = Cov(X, Z) +Cov(Y, Z).

Let X, Y, and Z be jointly distributed random variables. Prove that Cov(X + Y, Z) = Cov(X, Z) +Cov(Y, Z).

Step by Step Solution

★★★★★

3.29 Rating (155 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

CovX YZ XY Z XY Z XZ ... View full answer

blur-text-image
Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock
Step: 3 Unlock

Students Have Also Explored These Related Statistics Engineers Scientists Questions!

Q:

Let X and Y be jointly distributed random variables. This exercise leads you through a proof of the fact that 1 X,Y 1. a. Express the quantity V(X (X/Y) Y) in terms of X, Y, and Cov(X, Y ). b. Use...

Q:

X and Z are two jointly distributed random variables. Suppose you know the value of Z, but not the value of . Let X = E( X| Z) denote a guess of the value of X using the information on Z, and let W =...

Q:

Let X and Y be jointly distributed on the portion of the Cartesian plane between the curves y = x and y = x2. Let the joint density of X, Y be fX,Y(x, y) =8y/3x in this regions, and fX,Y (x, y) = 0...

Q:

Let X, Y, and Z be jointly continuous random variables. Assume that all conditional PDFs and expectations are well defined. E.g., when conditioning on X=x, assume that x is such that fx(x)>0. For...

Q:

Let X, Y, and Z be jointly continuous random variables. Assume that all conditional PDFs and expectations are well defined. E.g., when conditioning on X=x, assume that x is such that fx(x)>0. For...

Q:

Let X, Y, and Z be jointly continuous random variables. Assume that all conditional PDFs and expectations are well defined. E.g., when conditioning on X=x, assume that x is such that fx(x)>0. For...

Q:

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 E(Y) = 7 Var (X) = 9 Var (Y)...

Q:

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) = 0 E(Y) =-5 Var (X) = 13 Var (Y)...

Q:

5. Let X and Z be zero-mean, jointly Gaussian random variables with variances Ox and Oz, respectively. and correlation coefficient P. (a) Express Z as a linear combination of X and Gaussian r.v. Y...

Q:

Let X and Y be two jointly continuous random variables, with joint probability density function f(X,Y)(3': y) = 011m] (3)1[a1] (y) for some constant c > 0. (i) Determine the value of 0. (ii) Are X...

Q:

Why are welfare payments from a state social services agency nontaxable to the recipient while state unemployment benets are taxable?

Q:

Q.1 The air is compressed adiabatically in a combined piston-cylinder from 1 bar, 300 K to 10 bar, 600 K. Determine the work done, in kJ per kg of air, and the amount of entropy produced, in kJ/K per...

Q:

What are some potential problems with using barrel draw methods to select a simple random sample?

Q:

11. The annual return per dollar for two different investment instruments is the outcome of a bivariate random variable (X1, X2) with joint moment-generating function Mx(t) exp(u0 t :5t0 St), where...

Q:

The specific gravity of a substance is given by G = DS/DW, where DS is the density of the substance in kg/m3 and DW is the density of water, which is known to be 1000 kg/m3. The density of a...

Q:

Find the uncertainty in Y, given that X = 4.0 0.4 and a. Y = X2 b. Y =X c. Y = 1/X d. Y = ln X e. Y = eX f. Y = sin X (X is in units of radians)

Q:

Convert the following absolute uncertainties to relative uncertainties. a. 37.2 0.1 b. 8.040 0.003 c. 936 37 d. 54.8 0.3

Q:

Which of the following statements is not true? A. A purchase invoice is a source document that tells a business how much to pay a vendor. B.Revenues must always exceed expenses. C. On a correct trial...

Q:

des Compute yield-to-maturity for the following zero-coupon bonds: 1-year zero-coupon bond, traded currently at 990 dollars 2-years zero-coupon bond, traded currently at 955 dollars 3-years...

Q:

Synovec Co. is growing quickly. Dividends are expected to grow at a rate of 30 percent for the next three years, with the growth rate falling off to a constant 5 percent thereafter. If the required...