## Probability distributions (joint)

I have this question:

and 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 cant 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 :/