2) Suppose that X and Y has joint density function of bivariate normal distribution as follows: f(x, y) = 1 2π√1-p² - e 1 2(1-p²) (x²-2pxy + y²) 1(-30,00) (x) 1(-0,00) (X). Assume that the marginal distribution of random variables X and Y is N(0,1). Show that the conditional distribution of X given Y is N(py,1-p²).
2) Suppose that X and Y has joint density function of bivariate normal distribution as follows: f(x, y) = 1 2π√1-p² - e 1 2(1-p²) (x²-2pxy + y²) 1(-30,00) (x) 1(-0,00) (X). Assume that the marginal distribution of random variables X and Y is N(0,1). Show that the conditional distribution of X given Y is N(py,1-p²).
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Transcribed Image Text:2) Suppose that X and Y has joint density function of bivariate normal distribution as
follows:
1
27√1-p²
f(x, y) = -
e
1
{( x²_2pxy + y²)
2(1-0²) (18²2-
I(-20,00) (x)(-0,10) (Y).
Assume that the marginal distribution of random variables X and Y is N(0,1).
Show that the conditional distribution of X given Y is N(py,1-p²).
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