Stats doubt2

[The Villain]

Consider f(x,y)=1/8(6-x-y); 0<x<2
                                      2<y<4
find P(x+y<3)

[Homer Simpson]

getting 1/24

[The Villain]

Tsuki..The ans is 5/24

[Homer Simpson]

yep made a careless mistake. getting 5/24, not 1/24 - took 2<y<3-x and 0<x<1 to solve

[Shefali]

How did you solve tsuki?

[The Villain]

Thanxx Tsuki

[Anjali]

Plz explain tsuki ! How to go about such questions ?

[Homer Simpson]

This is a continuous joint pdf -

take, y<3-x

we know that y takes values between 2 and 4, thus, x lies between 0 and 1 for valid intervals. now that i have my two ranges, i need to take double integral with x and y values to find area/probability.