Question: Bivariate Normal Distribution Let (X, Y ) be Bivariate Normal with X N(0, ^2 1 ) and Y N(0, ^2 2 ) marginally and with

Bivariate Normal Distribution

Let (X, Y ) be Bivariate Normal with X N(0, ^2 1 ) and Y N(0, ^2 2 ) marginally and with Corr(X, Y ) = .

(a) Show that X, Y cX also follows a Bivariate Normal distribution for any constant c.

(b) Find a constant c such that Y cX is independent of X. ( Hint: Find c such that Cov(X, Y cX) = 0. Now argue why that also ensures independence.

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock blur-text-image
Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock
Step: 3 Unlock

Students Have Also Explored These Related Mathematics Questions!

Q:

Bivariate Normal Distribution Let (X, Y ) be Bivariate Normal with X N(0, 1 2 ) and Y N(0, 2 2 ) marginally and with Corr(X, Y ) = . (a) Show that X, Y cX also follows a Bivariate Normal distribution...

Q:

2) Consider the following joint probability density function 1 f(x, y) = = e 2(1-2) (x-2pxy+y) 3 x,yR, p-1, 1]. 2 1-p A special case of the bivariate normal distribution centered at (x, y) = (0, 0),...

Q:

Question: Following the principles of Epidemiologic inquiry, answer the following questions regarding one health determinant in Fredericksburg county in Virginia. www.countyhealthrankings.org,...

Q:

Please resolve. Jack and Sam are both taking a statistics class this summer. They decided to study separately for their exam. The probability that Jack will make an "A" in statistics is 0.6, and the...

Q:

public class RightTriangle ( public int hypotenuse () [ private int base: return this -hypotenuse; private int height; private int hypotenuse; public void metBase (int newBans) public RightTriangle...

Q:

What is the main difference between High-Low Method and Regression Analysis? A) They are the same B) Regression Analysis is used in aggressive periods, but High-Low Method is used always C) High-Low...

Q:

If we assume that n and nu are mutually independent for all t, the vectors n(t) are independently and identically distributed according to a bivariate normal distribution with mean [0,0]" and...

Q:

Prove Proposition 6.38 Su' (es) u(-1)' Proposition 6.38 Under the assumptions of the present section, let m = for all t = 1,..., T, and suppose that (log m,, log r) conditionally on F-1 follows a...

Q:

independent. A random vector (X, Y ) is said to be standard bivariate Gaussian if its joint density is given by: T f(x, y) = X exp E (27) V(1 + (EXY ) 2) Here E is the covariance matrix given by EXY...

Q:

Assuming a random effects model, show that E (SSB) = (b 1) 2 + k (b 1) 23 for the randomized complete block design.

Q:

The Kenya Tea Development Authority (KTDA) sells three brands of tea, Gold label (G), Quality label (Q) and National label (N).The companys marketing specialist has analyzed the switching habits of...

Q:

true of false use of LIFO provides a tax benefit in an industry where costs decrease as production increases

Q:

Required: 1. The company can purchase the equipment by borrowing $286,000 with a 22 -month, 12% installment note. Payments of $14,547.02 are due at the end of each month, and the first installment is...