If a=< 1, then P[X>X^2].... how is 1>1^2? That does not make sense to me.
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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.
I can never get anything right FFS
NVM.. after reading the problem again this was actually really simple lol.