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

  1. $\frac{1}{2}$
  2. 1
  3. 0
  4. $\frac{1}{3}$
  5. Information is insufficient.
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Best answer
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11 votes

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.

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