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

oppvarmet16

oppvarmet16

Answered question

2021-11-29

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

Answer & Explanation

Fachur

Fachur

Beginner2021-11-30Added 17 answers

We have:
joint density of X and Y
fxy(x,y)=67(x2+xy2) 0<x<1,0<y<2
1) P(x<1,y>1)
P(x<1,y>1)=x=01y=1267(x2+xy2) dy  dx 
P(x<1,y>1)=6701[x2y+x2y22]12 dx 
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
2) X and Y's marginal probability densities.
Marginal probability density of x
fx(x)=y=0267(x2+xy2) dy =67[x2y+x2y22]02=67(2x2+x)
fx(x)=67(2x2+x)
presently, marginal y-probability density
 

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