Solve b 3.6.14. Let Xi, X2, and Xs be three independent chi-square variables with rı, r2, and T3 degrees of freedom, res...

Question

Question

3.6.14. Let Xi, X2, and Xs be three independent chi-square variables with rı, r2, and T3 degrees of freedom, respectively. (a Solve b

math Statistics-And-Probability

Add a comment Improve this question Transcribed image text

Answer 1

Answer #1

n m, ブhis is ±ne defnuhmof F distai.bution ㄐㄚッx, xitx2- PLEASE LEAVE AN UPV0TE!!

Add a comment

Answer 2

Similar Homework Help Questions

7. Let Xn Xi++X2, where the Xi's are iid standard normal random variables (a) Show that Sn is a c...

7. Let Xn Xi++X2, where the Xi's are iid standard normal random variables (a) Show that Sn is a chi-square random variable with n de- grees of freedom. Hint: Show that X is chi-square with one degree of freedom, and then use Problem 6. (b) Find the pdf of (c) Show that T2 is a Rayleigh random variable. (d) Find the pdf for Ts. The random variable Ts is used to model the speed of molecules in a gas. It...
10) Suppose that X follows a chi-square distribution with m degrees of freedom and S=X+Y. Given...

10) Suppose that X follows a chi-square distribution with m degrees of freedom and S=X+Y. Given that S follows a chi-square distribution with m+n degrees of freedom, and X and Y are independent, show that y follows a chi-square distribution with n degrees of freedom.
Please solve these questions 1. Suppose that X1, X2, and Xs are random variables with common...

Please solve these questions 1. Suppose that X1, X2, and Xs are random variables with common mean μ and variance matrix Find E(X1 +2X1X2-4X2X3 + X ]. 2. If X1, X2,..., X, are independent random variables with common mean (n - 1)] is an μ and variances σ?, σ2, .. ., σ unbiased estimate of varf , prove that Σ,(X,-X)2/[n 3. Suppose that in Exercise 2 the variances are known. Let X,-Σ,wa, be an unbiased estimate of μ (i.e., Σί...

PROBLEM 8: It is easy to show with mgf's that the sum of independent chi-squared random...

PROBLEM 8: It is easy to show with mgf's that the sum of independent chi-squared random variables has a chi- squared distribution with degrees of freedom equal to the sum of the degrees of freedom associated with each of the random variables being summed. For example, if w (df -i) and all W's are independent, then Σ W,-X2 | df n(n+1 2 서 Now, suppose that X, N(i,i), and all X's are independent. Using your result in the previous problem...
3. (25 pts.) Let X1, X2, X3 be independent random variables such that Xi~ Poisson (A), i 1,2,3. Let N = X1 + X2+X3. (a)...

3. (25 pts.) Let X1, X2, X3 be independent random variables such that Xi~ Poisson (A), i 1,2,3. Let N = X1 + X2+X3. (a) What is the distribution of N? (b) Find the conditional distribution of (X1, X2, X3) | N. (c) Now let N, X1, X2, X3, be random variables such that N~ Poisson(A), (X1, X2, X3) | N Trinomial(N; pi,p2.ps) where pi+p2+p3 = 1. Find the unconditional distribution of (X1, X2, X3). 3. (25 pts.) Let X1,...
6. Suppose the covariances between Xi and X2 is 3, between Xi and Xs is 2, and between X2 and X i...

6. Suppose the covariances between Xi and X2 is 3, between Xi and Xs is 2, and between X2 and X is 1. Moreover, the standard deviations of Xi, X2, Xs are, 3,2.2, respectively (a) Write the 3x3 covariance (2) and correlation (R) matrices of the random vectorX(X, X2, X). (b) Show that for any scalars aï.аг, аз: Var(aiX1 +a2X2 + asXs- (c) Use the formula in (b) and compute the (nunerical) value of Varlai XXaA) for the following choices...

Let Xi Pn(2) and X2 Pn(5) be two independent random variables and it that y = Xi + X-Pn(7). is shown (a) Given Y-n, n 20, what are the possible values of X1? (b) Calculate the conditional distributio...

Let Xi Pn(2) and X2 Pn(5) be two independent random variables and it that y = Xi + X-Pn(7). is shown (a) Given Y-n, n 20, what are the possible values of X1? (b) Calculate the conditional distribution of Xi given Y-n for n 2 0. Let Xi Pn(2) and X2 Pn(5) be two independent random variables and it that y = Xi + X-Pn(7). is shown (a) Given Y-n, n 20, what are the possible values of X1? (b)...
Let Xi and X2 independent random variables, with distribution functions F1, and F2, respectively Let Y a Bernoulli random variable with parameter p. Suppose that Y, X1 and X2 are independent. Proof u...

Let Xi and X2 independent random variables, with distribution functions F1, and F2, respectively Let Y a Bernoulli random variable with parameter p. Suppose that Y, X1 and X2 are independent. Proof using the de finition of distribution function that the the distribution function of Z =Y Xit(1-Y)X2 is F = pF14(1-p)F2 Don't use generatinq moment functions, characteristic functions) Xi and X2 independent random variables, with distribution functions F1, and F2, respectively Let Y a Bernoulli random variable with parameter...
If X1, X2, and X3 are three independent Uniform random variables (Xi-Unif(0,1)) a) Use the convol...

If X1, X2, and X3 are three independent Uniform random variables (Xi-Unif(0,1)) a) Use the convolution integral to find density function of Z-x1+X2+X3. b) What is E[Z]? independent Uniform random variables (Xi-Unifo,1): If X1, X2, and X3 are three independent Uniform random variables (Xi-Unif(0,1)) a) Use the convolution integral to find density function of Z-x1+X2+X3. b) What is E[Z]? independent Uniform random variables (Xi-Unifo,1):

3) Let (x, y), (X2, y2), and (X3. Y3) be three points in R2 with X1...

3) Let (x, y), (X2, y2), and (X3. Y3) be three points in R2 with X1 < x2 < X3. Suppose that y = ax + by + c is a parabola passing through the three points (x1, yı), (x2, y), and (x3, Y3). We have that a, b, and c must satisfy i = ax + bx + C V2 = ax + bx2 + c y3 = ax} + bx3 + c Let D = x X2 1....

Solve b 3.6.14. Let Xi, X2, and Xs be three independent chi-square variables with rı, r2, and T3 degrees of freedom, res...

Homework Answers

Add Answer to:
Solve b 3.6.14. Let Xi, X2, and Xs be three independent chi-square variables with rı, r2, and T3 degrees of freedom, res...

Post as a guest

Earn Coins

7. Let Xn Xi++X2, where the Xi's are iid standard normal random variables (a) Show that Sn is a c...

10) Suppose that X follows a chi-square distribution with m degrees of freedom and S=X+Y. Given...

Please solve these questions 1. Suppose that X1, X2, and Xs are random variables with common...

PROBLEM 8: It is easy to show with mgf's that the sum of independent chi-squared random...

3. (25 pts.) Let X1, X2, X3 be independent random variables such that Xi~ Poisson (A), i 1,2,3. Let N = X1 + X2+X3. (a)...

6. Suppose the covariances between Xi and X2 is 3, between Xi and Xs is 2, and between X2 and X i...

Let Xi Pn(2) and X2 Pn(5) be two independent random variables and it that y = Xi + X-Pn(7). is shown (a) Given Y-n, n 20, what are the possible values of X1? (b) Calculate the conditional distributio...

Let Xi and X2 independent random variables, with distribution functions F1, and F2, respectively Let Y a Bernoulli random variable with parameter p. Suppose that Y, X1 and X2 are independent. Proof u...

If X1, X2, and X3 are three independent Uniform random variables (Xi-Unif(0,1)) a) Use the convol...

3) Let (x, y), (X2, y2), and (X3. Y3) be three points in R2 with X1...

Solve b 3.6.14. Let Xi, X2, and Xs be three independent chi-square variables with rı, r2, and T3 degrees of freedom, res...

Homework Answers

Add Answer to: Solve b 3.6.14. Let Xi, X2, and Xs be three independent chi-square variables with rı, r2, and T3 degrees of freedom, res...

Post as a guest

Earn Coins

Add Answer to:
Solve b 3.6.14. Let Xi, X2, and Xs be three independent chi-square variables with rı, r2, and T3 degrees of freedom, res...