Let X,Y be discrete random variables on a probability space. Prove or Disprove that:
X,Y iid --> P({X=Y})=0
Let $\displaystyle x$ take the value $\displaystyle 0$ with probability $\displaystyle 1/2$ and $\displaystyle 1$ with prob. $\displaystyle 1/2$
Let $\displaystyle y$ take the value $\displaystyle 0$ with probability $\displaystyle 1/2$ and $\displaystyle 1$ with prob. $\displaystyle 1/2$
and $\displaystyle p(x=a,y=b)=p(x=a)p(y=b),\ a$ and $\displaystyle b$ in $\displaystyle \{0,1\}$
Then the RV's $\displaystyle X$ and $\displaystyle Y$ are iid.
What is the probability that $\displaystyle x=1$, and $\displaystyle y=1$?
RonL