Let (X, Y) be a pair of jointly continuous random variables with joint p.d.f.3f (x, y) :=, 0sx< 1, 2²< y< 1.2'(a)Find the marginal p.d.f. fx(x) of X and the marginal p.d.f. fy (y) of Y.(Ь)Find the covariance Cov(X, Y) of X and Y.(c)Find the conditional p.d.f. fy|x(y|x) of Y given X = x, for any x E (0, 1).(d)Find the conditional expectation E(Y|X = 1/2) of Y given X = 1/2.2.

(a) The joint pdf is given by : f(x,y)=32, 0≤x≤1, x2≤y≤1 The marginal pdf of x is given by :…

Answered: Let (X, Y) be a pair of jointly…

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Let (X, Y) be a pair of jointly continuous random variables with joint p.d.f. f (x, y) 3 0

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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Question

Let (X, Y) be a pair of jointly continuous random variables with joint p.d.f.
3
f (x, y) :
=, 0sx< 1, 2²< y< 1.
2'
(a)
Find the marginal p.d.f. fx(x) of X and the marginal p.d.f. fy (y) of Y.
(Ь)
Find the covariance Cov(X, Y) of X and Y.
(c)
Find the conditional p.d.f. fy|x(y|x) of Y given X = x, for any x E (0, 1).
(d)
Find the conditional expectation E(Y|X = 1/2) of Y given X = 1/2.
2.

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