1. Let random variables X and Y are distributed as the joint normal distribution, whose density f is given as fxy(z,v) exp 2(1-p) (1) Prove that f fxx(x,y) dæ dy = 1. (i) Compute the marginal density fx(=) := | xr(z, v) dy. (ii) Compute the expectation E[XY]. What value of p makes it hold that E[XY]=E[X]E[Y]-
1. Let random variables X and Y are distributed as the joint normal distribution, whose density f is given as fxy(z,v) exp 2(1-p) (1) Prove that f fxx(x,y) dæ dy = 1. (i) Compute the marginal density fx(=) := | xr(z, v) dy. (ii) Compute the expectation E[XY]. What value of p makes it hold that E[XY]=E[X]E[Y]-
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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![1. Let random variables X and Y are distributed as the joint normal distribution, whose density f is
given as
fxx(2, v) =
exp
(1² + y° - 2pry)
2(1 p)
() Prove that f txx(E,y) dæ dy =1.
(11) Compute the marginal density
(ii) Compute the expectation E[XY]. What value of p makes it hold that E[XY) = E\X\EY.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F11d90570-efff-4b6e-9c36-90fa9e448a46%2F7ab18872-0a0b-4199-b4f1-a25734c200d2%2Fyavzsxk_processed.png&w=3840&q=75)
Transcribed Image Text:1. Let random variables X and Y are distributed as the joint normal distribution, whose density f is
given as
fxx(2, v) =
exp
(1² + y° - 2pry)
2(1 p)
() Prove that f txx(E,y) dæ dy =1.
(11) Compute the marginal density
(ii) Compute the expectation E[XY]. What value of p makes it hold that E[XY) = E\X\EY.
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