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Thread: Not understanding Uniform distribution example

  1. #1
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    Not understanding Uniform distribution example

    If a=< 1, then P[X>X^2].... how is 1>1^2? That does not make sense to me.
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  2. #2
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    Re: Not understanding Uniform distribution example

    Quote Originally Posted by math951 View Post
    If a=< 1, then P[X>X^2].... how is 1>1^2? That does not make sense to me.
    First, it does not say that $\bf{1>1^2}$.
    It does say that if $X\in (0,1)$ then $ \mathcal{P}(X^2<X)=1$.

    Because, $\forall a\in (0,1)[a^2<a]$ Proof:
    $ \begin{align*}0&<a<1 \\0<a^2&<a<1 \end{align*}$
    So the probability that $X^2<X$ is one.
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  3. #3
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    Re: Not understanding Uniform distribution example

    I can never get anything right FFS
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  4. #4
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    Re: Not understanding Uniform distribution example

    NVM.. after reading the problem again this was actually really simple lol.
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