Joint Probability Distributions

[Carla1985]

I have this question:

View attachment 690and I'm a little confused. To calculate joint distributions in the earlier questions i was using:$$P_{(\xi1,\xi2)}(x1,x2)=P_{(\xi1)}(x1)P_{(\xi2)}(x2)$$But that would mean that if:$$P_{(\xi1,\xi2)}(2,0)=0\ either\ P_{(\xi1)}(2)=0\ or\ P_{(\xi2)}(0)=0$$which can't be true in either case as $$P_{(\xi1,\xi2)}(1,0)\ isnt\ 0\ and\ neither\ is\ P_{(\xi1,\xi2)}(2,1)$$Can someone please explain what I'm missing. Thanks :/

 

[Carla1985]

Nevermind, I found my mistake. This was only for independent variables, which these obviously aren't :)