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.