Joint Probability Distribution - Example

Example

Consider the roll of a die and let if the number is even (i.e.; 2,4, or 6) and otherwise. Furthermore, let if the number is prime (i.e.; 2, 3 or 5) and otherwise. Then, the joint distribution of and is

\mathrm{P}(A=0,B=0)=P\{1\}=\frac{1}{6},\; \mathrm{P}(A=1,B=0)=P\{4,6\}=\frac{2}{6}
\mathrm{P}(A=0,B=1)=P\{3,5\}=\frac{2}{6},\; \mathrm{P}(A=1,B=1)=P\{2\}=\frac{1}{6}


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