REVIEW Review Conditional pdf Let(Y1,., YN) have joint pdf f(31,.. JN). Let f(3J+1, .. yN)be the marginal pdf of(y+1,……,YN). The conditional pdf of y1,…, Y, given y+1,…, YN is defined by JJ3J+1 f(+1,…3N) for f(3J+ yN)>0 Example 1 Let Y1 and Y2 be discrete r U. s with bivariate paf f (y1, 32) (m+v)/9,y=0,1,2and otherwise The f(3) 1-0(0,0)=份+=当社,m=012 The conditional paf of y2 gien y1=g is f(y2)-+2 f(32|)= 0,1 otherwise Example 2 Let Y1 and Y2 be continuo us T U.s with bivariate paf 2,0<<<1 f() m20=2(1-m),0<m<1 he f(g2v) f0<a<<1 otherwise (a faREVIEW 1 Review Conditional pdf Let (Y1, · · · , YN ) have joint pdf f (y1, · · · , yN ). Let f (yJ+1, · · · , yN ) be the marginal pdf of (YJ+1, · · · , YN ). The conditional pdf of Y1, · · · , YJ given YJ+1, · · · , YN is defined by f (y1, · · · yJ |yJ+1, · · · yN ) = f (y1, · · · , yJ+1, · · · , yN ) f (yJ+1, · · · yN ) for f (yJ+1, · · · , yN ) > 0. Example 1 Let Y1 and Y2 be discrete r.v.s with bivariate pdf f (y1, y2) =
(y1 + y2) /9 , y1 = 0, 1, 2 and y2 = 0, 1 0 , otherwise. The marginal pdf of Y1 is f (y1) =
1 y2=0 f (y1, y2) = y1 9 + y1+1 9 = 2y1+1 9 , y1 = 0, 1, 2 0 , otherwise. The conditional pdf of Y2 given Y1 = y1 is f (y2|y1) = f(y1,y2) f(y1) = y1+y2 2y1+1 , y2 = 0, 1 0 , otherwise. Example 2 Let Y1 and Y2 be continuous r.v.s with bivariate pdf f (y1, y2) =
2 , if 0 < y1 < y2 < 1 0 , otherwise. Then f (y1) =
 1 y1 2dy2 = 2 (1 − y1) , 0 < y1 < 1 0 , otherwise. f (y2|y1) =
1 1−y1 , if 0 < y1 < y2 < 1 0 , otherwise. (a function of y1)