Homework Answers
TOPIC: Use of mean vector and dispersion matrix to find the required values.
Add Answer to:
Given three random variables Given three random variables Xi, X2, and X such that X[Xi X2...
Given three random variables Xi, X2, and X such that X[Xi X2 X 20 -1 3...
Given three random variables Xi, X2, and X such that X[Xi X2 X 20 -1 3 1 0.5 1 E [X]-μ | 0 | and var(X)=Σー| 0 0.5 | com pute: 2 c) var(X2-X3 (d) var(X2 + X3) (e) cov(4X2 +X1,3Xi - 2X3)
how to calculate cov(x1,x2), cov(x2,x3),cov(x3,x1)? and how to calculate var(x1),var(x2),var(x3)? Given three random variables Xi, X2,...
how to calculate cov(x1,x2), cov(x2,x3),cov(x3,x1)?
and how to calculate var(x1),var(x2),var(x3)?
Given three random variables Xi, X2, and X such that X[Xi X2 X 20 -1 E [X] ,1-10 | and var(X)=Σ-| 0 3 0. 1 0.5 1 compuite: 2
1 [3]. Let X1,X2, X3 be iid random variables with the common mean --1 2-4 and...
1 [3]. Let X1,X2, X3 be iid random variables with the common mean --1 2-4 and variance σ Find (a) E (2X1 - 3X2 + 4X3); (b) Var(2X1 -4X2); (c) Cov(Xi - X2, X1 +2X2).
2. The random variables X1, X2 and X3 are independent, with Xi N(0,1), X2 N(1,4) and...
2. The random variables X1, X2 and X3 are independent, with Xi N(0,1), X2 N(1,4) and X3 ~ N(-1.2). Consider the random column vector X-Xi, X2,X3]T. (a) Write X in the form where Z is a vector of iid standard normal random variables, μ is a 3x vector, and B is a 3 × 3 matrix. (b) What is the covariance matrix of X? (c) Determine the expectation of Yi = Xi + X3. (d) Determine the distribution of Y2...
3. You may use this fact throughout: For any scalars a, a2,a3 and random variables .X2, X3: (a) I...
3. You may use this fact throughout: For any scalars a, a2,a3 and random variables .X2, X3: (a) If Cov (Xi, X2) Cov (X2, X3)-p, Cov (Xi, X3)-p and Var(X1,2,3, then write the 3 x 3 covariance matrix of the random vector X = (X1,X2,X3). (b) Compute Var(Xi X2+X3) when p 0.6. (e) Mark is interested in forecasting X using the linear predictor &bbX He realizes the forecast error is X - X X bX2 -bX and a great way...
Let X- (Xi, X2,X3) be an absolutely continuous random vector with the joint probability density function...
Let X- (Xi, X2,X3) be an absolutely continuous random vector with the joint probability density function elsewhere. Calculate 1. the probability of the event A -(Xs 3. the probability density function xx (,s) of the (XX)-marginal 4. the probability density function fx, () of the Xi-marginal, and the probability density function fx (r3) of the X3-marginal 5. Are Xi and X independent random variables? 6. E(Xi) and Var(X) 8. the covariance cov(Xi, X3) of Xi and X,3 9. Which elements...
2 0 -1 EIX) = μ = | 0 | and var(X) Σ _ | 0...
2 0 -1 EIX) = μ = | 0 | and var(X) Σ _ | 0 -1 0.5 3 0.5 | compute: (a) E[Xi +Xs] (c) var(X2- X3) d var(X2 + X) (e) cov(4X2 +X1,3Xi -2X)
2 0 -1 EIX) = μ = | 0 | and var(X) Σ _ | 0...
2 0 -1 EIX) = μ = | 0 | and var(X) Σ _ | 0 -1 0.5 3 0.5 | compute: (a) E[Xi +Xs] (c) var(X2- X3) d var(X2 + X) (e) cov(4X2 +X1,3Xi -2X)
Let X1, X2, and X3 be uncorrelated random variables, each with 4. (10 points) Let Xi,...
Let X1, X2, and X3 be uncorrelated random variables, each
with
4. (10 points) Let Xi, X2, and X3 be uncorrelated random variables, each with mean u and variance o2. Find, in terms of u and o2 a) Cov(X+ 2X2, X7t 3X;) b) Cov(Xrt X2, Xi- X2)
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):
Given three random variables Xi, X2, and X such that X[Xi X2 X 20 -1 3 1 0.5 1 E [X]-μ | 0 | and var(X)=Σー| 0 0.5 | com pute: 2 c) var(X2-X3 (d) var(X2 + X3) (e) cov(4X2 +X1,3Xi - 2X3)
how to calculate cov(x1,x2), cov(x2,x3),cov(x3,x1)?
and how to calculate var(x1),var(x2),var(x3)?
Given three random variables Xi, X2, and X such that X[Xi X2 X 20 -1 E [X] ,1-10 | and var(X)=Σ-| 0 3 0. 1 0.5 1 compuite: 2
1 [3]. Let X1,X2, X3 be iid random variables with the common mean --1 2-4 and variance σ Find (a) E (2X1 - 3X2 + 4X3); (b) Var(2X1 -4X2); (c) Cov(Xi - X2, X1 +2X2).
2. The random variables X1, X2 and X3 are independent, with Xi N(0,1), X2 N(1,4) and X3 ~ N(-1.2). Consider the random column vector X-Xi, X2,X3]T. (a) Write X in the form where Z is a vector of iid standard normal random variables, μ is a 3x vector, and B is a 3 × 3 matrix. (b) What is the covariance matrix of X? (c) Determine the expectation of Yi = Xi + X3. (d) Determine the distribution of Y2...
3. You may use this fact throughout: For any scalars a, a2,a3 and random variables .X2, X3: (a) If Cov (Xi, X2) Cov (X2, X3)-p, Cov (Xi, X3)-p and Var(X1,2,3, then write the 3 x 3 covariance matrix of the random vector X = (X1,X2,X3). (b) Compute Var(Xi X2+X3) when p 0.6. (e) Mark is interested in forecasting X using the linear predictor &bbX He realizes the forecast error is X - X X bX2 -bX and a great way...
Let X- (Xi, X2,X3) be an absolutely continuous random vector with the joint probability density function elsewhere. Calculate 1. the probability of the event A -(Xs 3. the probability density function xx (,s) of the (XX)-marginal 4. the probability density function fx, () of the Xi-marginal, and the probability density function fx (r3) of the X3-marginal 5. Are Xi and X independent random variables? 6. E(Xi) and Var(X) 8. the covariance cov(Xi, X3) of Xi and X,3 9. Which elements...
2 0 -1 EIX) = μ = | 0 | and var(X) Σ _ | 0 -1 0.5 3 0.5 | compute: (a) E[Xi +Xs] (c) var(X2- X3) d var(X2 + X) (e) cov(4X2 +X1,3Xi -2X)
2 0 -1 EIX) = μ = | 0 | and var(X) Σ _ | 0 -1 0.5 3 0.5 | compute: (a) E[Xi +Xs] (c) var(X2- X3) d var(X2 + X) (e) cov(4X2 +X1,3Xi -2X)
Let X1, X2, and X3 be uncorrelated random variables, each
with
4. (10 points) Let Xi, X2, and X3 be uncorrelated random variables, each with mean u and variance o2. Find, in terms of u and o2 a) Cov(X+ 2X2, X7t 3X;) b) Cov(Xrt X2, Xi- X2)
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):
Most questions answered within 3 hours.
-
1. When can parametric and non-parametric statistical tests be
used?
A. Parametric?
The independent variable is...
asked 2 minutes ago -
How can bacteria resist killing from cationic antimicrobial
peptides (CAMPs)? Choose all that apply. a. Use...
asked 9 minutes ago -
As an economic term, what is the definition of :Technological
Trends? Please try and keep the...
asked 10 minutes ago -
Labor demand will be less elastic in those labor markets in
which:
A.
the price elasticity...
asked 11 minutes ago -
5 situations are listed below and 8 reduction chemicals are
listed A-H below, match the letters...
asked 17 minutes ago -
1. If more spouses decide to quit their jobs to stay home with
their young children...
asked 20 minutes ago -
Please use algebraic manipulation to prove the following
statement:
x'y'z' + x'yz' + x'yz + xyz'...
asked 21 minutes ago -
3.Another patient has a family history in which:
1. the disease was equally distributed among the...
asked 24 minutes ago -
If you are the TM of a shipper of cooking oil the sales
department wants to...
asked 22 minutes ago -
NEED THIS URGENTLY PLEASEEE
Suppose a fair coin is tossed 5 times and the result are...
asked 31 minutes ago -
Find the magnetic field B produced by several circular loops of
which has a radius given...
asked 39 minutes ago -
A mole of monatomic ideal gas is expanded from 0.45 L to 0.75L
at an external...
asked 38 minutes ago