The joint density of X and Y is given by,f_{XY}(x,y)=\frac{6}{7}(x^{2}+\frac{xy}{2})\

oppvarmet16 2021-11-29 Answered

The joint density of X and Y is given by,
fXY(x,y)=67(x2+xy2) 0<x<1,0<y<2
a) Calculate P(X<1,Y>1)
b) Find the marginal probability distributions of X and Y.
c) Find the conditional probability density function of Y given X=0.5 and calculate P(Y<1/X=0.5)

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Expert Answer

Fachur
Answered 2021-11-30 Author has 17 answers

Given:
joint density of X and Y
fxy(x,y)=67(x2+xy2) 0<x<1,0<y<2
a) P(x<1,y>1)
P(x<1,y>1)=x=01y=1267(x2+xy2)dydx
P(x<1,y>1)=6701[x2y+x2y22]12dx
P(x<1,y>1)=6701(x2+3x4)dx=67[x33+34x22]01=67×1724=102168
=0.6071
P(x<1,y>1)=0.6071
b) Marginal probability density of x and y.
Marginal probability density of x
fx(x)=y=0267(x2+xy2)dy=67[x2y+x2y22]02=67(2x2+x)
fx(x)=67(2x2+x)
now, Marginal probability density of y

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