Re: Discussion Problem_(30)

Posted by Sinistral on Jun 05, 2013; 4:00pm
URL: http://discussion-forum.276.s1.nabble.com/Discussion-Problem-30-tp7581664p7581812.html

plotting x+y<1 [the domain of f(x,y) ] and 2x+3y<1 (the region whose probability needs to be calculated).
seeing the overlapping area.

by observing the overlapping area it is seen that the area of interest is  2x+3y<1 in the first quadrant (since it is given that x>0 , y>0)

so P(2X+3Y<1) = Integral [x= 0 to 1/2] Integral [ y=0 to (1-2x)/3] f(x,y) dy dx.
                     = 13/36