I tried to solve the same using $E(x^2)-[E(x)]^2$, but the answers I found come out to be negative.
2026-04-05 14:56:50.1775401010
Determine the variance of $X$ given the probabilty distributive function $f(x) = (1-x^2)$ for $0\le x\le 2$.
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$f$ is not a valid probability density function - one requirement is that for any event $E$, $P(E)\in[0,1]$. However, $P(1.5)<0$ for example and so the question is impossible.