Two random variables $X$ and $Y$ are said to be Independent and Identically distributed (ie. IID) **iff**

$F_X$ and $F_Y$ is CDF of Random variable $X$ and $Y$ respectively.

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13 votes

Let $X$ and $Y$ be two independent and identically distributed random variables. Then $P\left ( X> Y \right )$ is.

- $\frac{1}{2}$
- 1
- 0
- $\frac{1}{3}$
- Information is insufficient.

Two random variables $X$ and $Y$ are said to be Independent and Identically distributed (ie. IID) **iff**

$F_X$ and $F_Y$ is CDF of Random variable $X$ and $Y$ respectively.

Ref: wiki source

1

11 votes

Best answer

Let the probability $P({X = Y}) > 0$. This can happen if $X$ and $Y$ are discrete random variables. Also, if $X$ and $Y$ are continuous random variables, it could be that some values have a non-zero probability of getting selected.

Then $P({X>Y}) = P({Y>X}) = \dfrac{1 - P({X=Y})}{2}$

**Since nothing is said about the value of **$P({X=Y})$,** the correct answer will be option e. Information is insufficient.**