Question
If the joint pdf X and Y is given by f(x,y) = (1-e-x)(1-e-y) , for x>0,y>0
0 , otherwise Find P(1<x<3,1<y<2).
0 , otherwise Find P(1<x<3,1<y<2).
Answers
Damon
(1-e^-x) integral (1-e^-y) dy from 1 to 2
(1-e^-x) [ y + e^-y ] at 2 - at 1
(1-e^-x) [ 1 + (e^-2 - e^-1) ]
(1-e^-x) [ .767 ]
integrate that dx from 1 to 3
[ .767 ][ x + e^-x] at 3 - at 1
[ .767 ] [ 2 + (e^-3 - e^-1) ]
[ .767 ] [ 1.68 ]
1.29
divide by area to normalize
area = 2*1 = 2
1.29/2 = .645
(1-e^-x) [ y + e^-y ] at 2 - at 1
(1-e^-x) [ 1 + (e^-2 - e^-1) ]
(1-e^-x) [ .767 ]
integrate that dx from 1 to 3
[ .767 ][ x + e^-x] at 3 - at 1
[ .767 ] [ 2 + (e^-3 - e^-1) ]
[ .767 ] [ 1.68 ]
1.29
divide by area to normalize
area = 2*1 = 2
1.29/2 = .645