Question

Suppose that X1,X2 and X3 are independent random variables with common mean E(Xi) = μ and...

Suppose that X1,X2 and X3 are independent random variables with common mean E(Xi) = μ and variance Var(Xi) = σ2. Let V= X2−X3 and W = X1− 2X2 + X3.

(a) Find E(V) and E(W).

(b) Find Var(V) and Var(W).

(c) Find Cov(V,W).

(d) Find the correlation coefficient ρ(V,W). Are V and W independent?

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
Suppose that X1, X2, . . . , Xn are independent identically distributed random variables with...
Suppose that X1, X2, . . . , Xn are independent identically distributed random variables with variance σ2. Let Y1 = X2 +X3 , Y2 = X1 +X3 and Y3 = X1 + X2. Find the following : (in terms of σ2) (a) Var(Y1) (b) cov(Y1 , Y2 ) (c) cov(X1 , Y1 ) (d) Var[(Y1 + Y2 + Y3)/2]
Suppose that X1, X2, X3 are independent, have mean 0 and Var(Xi) = i. Find Cov(X1...
Suppose that X1, X2, X3 are independent, have mean 0 and Var(Xi) = i. Find Cov(X1 − X2, X2 + X3). .For X1, X2, X3,  find ρ(X1−X2, X2+ X3).
5. Let X1, X2, . . . be independent random variables all with mean E(Xi) =...
5. Let X1, X2, . . . be independent random variables all with mean E(Xi) = 7 and variance Var(Xi) = 9. Set Yn = X1 + X2 + · · · + Xn n (n = 1, 2, 3, . . .) (a) Find E(Y2) and E(Y5). (b) Find Cov(Y2, Y5). (c) Find E (Y2 | X1). (d) How should your answers from parts (a)–(c) be modified if the numbers “2”, “5”, “7” and “9” are replaced by m,...
Let x1, x2 x3 ....be a sequence of independent and identically distributed random variables, each having...
Let x1, x2 x3 ....be a sequence of independent and identically distributed random variables, each having finite mean E[xi] and variance Var（xi）. a）calculate the var （x1+x2） b）calculate the var（E[xi]） c） if n-> infinite, what is Var（E[xi]）？
Suppose X1, X2, X3, and X4 are independent and identically distributed random variables with mean 10...
Suppose X1, X2, X3, and X4 are independent and identically distributed random variables with mean 10 and variance 16. in addition, Suppose that Y1, Y2, Y3, Y4, and Y5are independent and identically distributed random variables with mean 15 and variance 25. Suppose further that X1, X2, X3, and X4 and Y1, Y2, Y3, Y4, and Y5are independent. Find Cov[bar{X} + bar{Y} + 10, 2bar{X} - bar{Y}], where bar{X} is the sample mean of X1, X2, X3, and X4 and bar{Y}...
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)}
Let X1, X2 be two normal random variables each with population mean µ and population variance...
Let X1, X2 be two normal random variables each with population mean µ and population variance σ2. Let σ12 denote the covariance between X1 and X2 and let ¯ X denote the sample mean of X1 and X2. (a) List the condition that needs to be satisfied in order for ¯ X to be an unbiased estimate of µ. (b) [3] As carefully as you can, without skipping steps, show that both X1 and ¯ X are unbiased estimators of...
Let X1, X2, X3, and X4 be mutually independent random variables from the same distribution. Let...
Let X1, X2, X3, and X4 be mutually independent random variables from the same distribution. Let S = X1 + X2 + X3 + X4. Suppose we know that S is a Chi-Square random variable with 2 degrees of freedom. What is the distribution of each of the Xi?
Let X1, X2,... be a sequence of independent random variables distributed exponentially with mean 1. Suppose...
Let X1, X2,... be a sequence of independent random variables distributed exponentially with mean 1. Suppose that N is a random variable, independent of the Xi-s, that has a Poisson distribution with mean λ > 0. What is the expected value of X1 + X2 +···+ XN2? (A) N2 (B) λ + λ2 (C) λ2 (D) 1/λ2
Let X1, X2, X3 be a random sample from a population. The distribution of the population...
Let X1, X2, X3 be a random sample from a population. The distribution of the population has a parameter θ, and it is known that E[Xi] = 2θ and Var[Xi] = σ2 for i = 1,2,3. Consider the following two point estimators for θ: W1= (1/8)X1+ (1/4)X2+ (1/8)X3 and W2= (1/6)X1+ (1/4)X2+ (1/12)X3 Which is the better estimator for θ? Why?
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT