Question

Let X and Y be jointly distributed random variables with means, E(X) = 1, E(Y) =...

Let X and Y be jointly distributed random variables with means, E(X) = 1, E(Y) = 0, variances, Var(X) = 4, Var(Y ) = 5, and covariance, Cov(X, Y ) = 2.

Let U = 3X-Y +2 and W = 2X + Y . Obtain the following expectations:

A.) Var(U):

B.) Var(W):

C. Cov(U,W):

ans should be 29, 29, 21 but I need help showing how to solve.

Math   Statistics-And-Probability   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Calculate the quantity of interest please. a) Let X,Y be jointly continuous random variables generated as...
Calculate the quantity of interest please. a) Let X,Y be jointly continuous random variables generated as follows: Select X = x as a uniform random variable on [0,1]. Then, select Y as a Gaussian random variable with mean x and variance 1. Compute E[Y ]. b) Let X,Y be jointly Gaussian, with mean E[X] = E[Y ] = 0, variances V ar[X] = 1,V ar[Y ] = 1 and covariance Cov[X,Y ] = 0.4. Compute E[(X + 2Y )2].
Let X and Y denote be as follows: E(X) = 10, E(X2) = 125, E(Y) =...
Let X and Y denote be as follows: E(X) = 10, E(X2) = 125, E(Y) = 20, Var(Y) =100 , and Var(X+Y) = 155. Let W = 2X-Y and let T = 4Y-3X. Find the covariance of W and T.
Let X and Y be independent and identically distributed random variables with mean μ and variance...
Let X and Y be independent and identically distributed random variables with mean μ and variance σ2. Find the following: a) E[(X + 2)2] b) Var(3X + 4) c) E[(X - Y)2] d) Cov{(X + Y), (X - Y)}
If X, Y are random variables with E(X) = 2, Var(X) = 3, E(Y) = 1,...
If X, Y are random variables with E(X) = 2, Var(X) = 3, E(Y) = 1, Var(Y) =2, ρX,Y = −0.5 (a) For Z = 3X − 1 find µZ, σZ. (b) For T = 2X + Y find µT , σT (c) U = X^3 find approximate values of µU , σU
Suppose that X and Y are two jointly continuous random variables with joint PDF ??,(?, ?)...
Suppose that X and Y are two jointly continuous random variables with joint PDF ??,(?, ?) = ??                     ??? 0 ≤ ? ≤ 1 ??? 0 ≤ ? ≤ √?                     0                        ??ℎ?????? Compute and plot ??(?) and ??(?) Are X and Y independent? Compute and plot ??(?) and ???(?) Compute E(X), Var(X), E(Y), Var(Y), Cov(X,Y), and Cor.(X,Y)
Let X and Y be independent and normally distributed random variables with waiting values E (X)...
Let X and Y be independent and normally distributed random variables with waiting values E (X) = 3, E (Y) = 4 and variances V (X) = 2 and V (Y) = 3. a) Determine the expected value and variance for 2X-Y Waiting value µ = Variance σ2 = σ 2 = b) Determine the expected value and variance for ln (1 + X 2) c) Determine the expected value and variance for X / Y
Uncorrelated and Gaussian does not imply independent unless jointly Gaussian. Let X ∼N(0,1) and Y =...
Uncorrelated and Gaussian does not imply independent unless jointly Gaussian. Let X ∼N(0,1) and Y = WX, where p(W = −1) = p(W = 1) = 0 .5. It is clear that X and Y are not independent, since Y is a function of X. a. Show Y ∼N(0,1). b. Show cov[X,Y ]=0. Thus X and Y are uncorrelated but dependent, even though they are Gaussian. Hint: use the definition of covariance cov[X,Y]=E [XY] −E [X] E [Y ] and...
8) X1X1 and X2X2 are two random variables that are jointly distributed such that E(X1)=8E(X1)=8, E(X2)=12E(X2)=12,...
8) X1X1 and X2X2 are two random variables that are jointly distributed such that E(X1)=8E(X1)=8, E(X2)=12E(X2)=12, Var(X1)=2Var(X1)=2, Var(X2)=3Var(X2)=3 and Cov(X1,X2)=−1Cov(X1,X2)=−1. Let Z=5X1−4X2−5Z=5X1−4X2−5. Compute E(Z)E(Z). Compute Var(Z)Var(Z). Compute Corr(X1,X2)Corr(X1,X2). Show all your working.
Let X and Y be jointly continuous random variables with joint density function f(x, y) =...
Let X and Y be jointly continuous random variables with joint density function f(x, y) = c(y^2 − x^2 )e^(−2y) , −y ≤ x ≤ y, 0 < y < ∞. (a) Find c so that f is a density function. (b) Find the marginal densities of X and Y . (c) Find the expected value of X
Consider two random variables X and Y such that E(X)=E(Y)=120, Var(X)=14, Var(Y)=11, Cov(X,Y)=0. Compute an upper...
Consider two random variables X and Y such that E(X)=E(Y)=120, Var(X)=14, Var(Y)=11, Cov(X,Y)=0. Compute an upper bound to P(|X−Y|>16)
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT