Re: joint probability question

Posted by knowpraveen on Jun 10, 2016; 5:02pm
URL: http://discussion-forum.276.s1.nabble.com/joint-probability-question-tp7601363p7601368.html

Are you talking about the 3rd question in the image? This could solved graphically. Plot a graph of X+Y=1 since we are given the density function.

It's obviously a uniform distribution function, the area of the region under consideration is 1/2, therefore the density turns out to be 1/(1/2) =2 for x>0, y>0 and X+Y<1. I hope, the question stands clear now. So, for P(X<2Y) Draw another line X-2Y=0 which is a positively sloped line passing through the origin meeting the X+Y=1 line at (2/3,1/3). Integration (1-x-x/2) from 0 to 2/3 which yields 1/3. Hence the probability of the case in question is 1/3/(1/2) = 2/3

Correct me if I'm wrong.