Suppose that the random variables Y1 and Y2 have a joint probability distribution function f(y1, y2) given by
f(y1,y2)= 0<=y1<=y2, y1+y2<=2 and f(y1,y2)=0 elsewhere
(A) What is the probability that Y1 + Y2 is less than 1?
for this question, i have hard time findthe region of my integration, it seems like i need to use separate integral to do this, if we do it as dy2dy1 order, then y2 goes from y1 to 1-y1, but then y2 go from 0 to to separate function, so do i need to do it twice?
i have drawn the region, but y1 would go to something depends on y2 eventually, it will end up with a function of y2, but we need a number here
we are given the answer is 1/32, i know y2 goes from 0 to y1 to 1-y1, but y1 will goes from 0 to some 1-y2, and 0 to y2, which will end up with a function of y2