So I have a PMF for $(X,Y)$ given by this tabel
\begin{equation}
\begin{array}{l|cccc}
& Y=1 & Y=2 & Y=3 & Y=4 \\
\hline X=1 & 0.04 & 0.07 & 0.10 & 0.01 \\
X=2 & 0.17 & 0.13 & 0.05 & 0.03 \\
X=3 & 0.06 & 0.10 & 0.08 & 0.02 \\
X=4 & 0.05 & 0.05 & 0.03 & 0.01
\end{array}
\end{equation}
I'm ask two find out whether $X$ and $Y$ have the same distribution or not.
But what does this mean? Does it mean that $P(X=x)=P(Y=y), \: \forall x,y, \: x=y$? I'm actually not sure how to formulate mathematically (notation). Use use the Blitzstein Hwang textbook, but I could not find a definition in this book.
Kind regards
Best Answer
If $X,Y$ are both random variables that only take values in $\{1,2,3,4\}$ then they have the same distribution if $$P(X=k)=P(Y=k)\text{ for every }k\in\{1,2,3,4\}$$
So to be found and compared are values $P(X=k)$ (summation of row $k$) and $P(Y=k)$ (summation of column $k$).