Query regarding joint distribution

Question

I came across a question which I never seen before, I just need guidance to which specific topic in probability such questions belongs, so that I can have a look at them out of curiosity. Here's the question :

.

Answer 1

I would assume geometric probability means a measure proportional to a length of an interval. So I would assume the intervals of length $1$ in $[-3,3]$ each have probability $\frac16$

So I think you have the joint density

   ω in interval    (X, Y)  Probability  
     -3 to -2       (0, 2)     1/6
     -2 to -1       (1, 1)     1/6 
     -1 to  0       (2, 0)     1/6 
      0 to  1       (2, 1)     1/6     
      1 to  2       (1, 2)     1/6  
      2 to  3       (0, 0)     1/6 

$X$ and $Y$ are not independent: can you see why not?