Question

Let x1 and x2 be random vektor such that x1+x2 and x1-x2 are independent and each...

Let x1 and x2 be random vektor such that x1+x2 and x1-x2 are independent and each normal distributed. Show that the random variable vector X=(x1,x2)' is distributed bivariate normal and determine its expected value and covariance matrix

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
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,... 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 X = (X1, X2) T be a two-dim random vector, and (R, Θ) be its...
Let X = (X1, X2) T be a two-dim random vector, and (R, Θ) be its polar coordinates, i.e. X1 = R cos(Θ) and X2 = R sin(Θ). Show that X is spherically symmetric if and only if R and Θ are independent, and Θ ∼Uniform(0, 2π).
Suppose that X1 and X2 are independent standard normal random variables. Show that Z = X1...
Suppose that X1 and X2 are independent standard normal random variables. Show that Z = X1 + X2 is a normal random variable with mean 0 and variance 2.
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]）？
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 and X2 be independent random variables such that X1 ∼ P oisson(λ1) and X2...
Let X1 and X2 be independent random variables such that X1 ∼ P oisson(λ1) and X2 ∼ P oisson(λ2). Find the distribution of Y = X1 + X2.s
Let X1, X2, X3 be independent random variables, uniformly distributed on [0,1]. Let Y be the...
Let X1, X2, X3 be independent random variables, uniformly distributed on [0,1]. Let Y be the median of X1, X2, X3 (that is the middle of the three values). Find the conditional CDF of X1, given the event Y = 1/2. Under this conditional distribution, is X1 continuous? Discrete?
Consider the bivariate random vector x = x1 x2 ∼ N2 µ1 µ2 , σ 2...
Consider the bivariate random vector x = x1 x2 ∼ N2 µ1 µ2 , σ 2 1 ρσ1σ2 ρσ1σ2 σ 2 2 1. Expand the matrix form of the density function to get the usual bivariate normal density involving σ1, σ2, ρ and exponential terms in (x1 1µ1) 2 ,(x1 1µ2) and (x2 2µ2) 2 . 2. Explain what happens in the following scenarios: (a) ρ = 0 (b) ρ = 1 (c) ρ = =1 1
Let each of the independent random variables X1 and X2 have the density function f(x) -...
Let each of the independent random variables X1 and X2 have the density function f(x) - e^-x for 0<x< inf., and f(x) = 0, otherwise. What is the joint density of Y1 = X1 and Y2 = 2X1 + 3X2 and the domain on which this density is positive?
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT