Problem: Two random variables

Problem

$S={a,b}$ . $P\left( \{ a \} \right)=P\left( \{ b \} \right)=1/2$ . $X\left( a \right)=0, X\left( b \right)=1$ . $Y\left( a \right)=0, Y\left( b \right)=1$

• Find the pmf of $X$ and the pmf of $Y$ . Are they the same?
• Are $X$ and $Y$ the same random variable?

Main point: Two random variables having the same distribution are not necessarily equal.