# Thread: Discrete Random Variables

1. ## Discrete Random Variables

Let X,Y be discrete random variables on a probability space. Prove or Disprove that:

X,Y iid --> P({X=Y})=0

2. Originally Posted by TXGirl
Let X,Y be discrete random variables on a probability space. Prove or Disprove that:

X,Y iid --> P({X=Y})=0
Let $x$ take the value $0$ with probability $1/2$ and $1$ with prob. $1/2$

Let $y$ take the value $0$ with probability $1/2$ and $1$ with prob. $1/2$

and $p(x=a,y=b)=p(x=a)p(y=b),\ a$ and $b$ in $\{0,1\}$

Then the RV's $X$ and $Y$ are iid.

What is the probability that $x=1$, and $y=1$?

RonL