Joint pdf calculation - Dept. of Statistics, Texas A&M University
Joint pdf calculation
Example 1 Consider random variables X,Y with pdf f(x,y) such that
8 <
6x2y;
0 < x < 1; 0 < y < 1
f (x; y) = : 0;
: otherwise.
Figure1. f(x; y)j0 < x < 1; 0 < y < 1g
Note that f (x; y) is a valid pdf because
P ( 1 < X < 1; 1 < Y < 1) = P (0 < X < 1; 0 < Y < 1) Z1 Z1
=
f (x; y)dxdy
11
Z1 Z1 = 6 x2ydxdy
0
Z1
0
8 ................
................
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