# Thread: Not understanding Uniform distribution example

1. ## 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.

2. ## Re: Not understanding Uniform distribution example

Originally Posted by math951
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.

3. ## Re: Not understanding Uniform distribution example

I can never get anything right FFS

4. ## Re: Not understanding Uniform distribution example

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