(a)[3]
Show that, in fact, $a = \frac{2}{b^2}$.
(b)[6]
Show that, indeed, $\mathrm{P}(X < \mathrm{E}(X)) = \frac{4}{9}$.
Mathematics 9709 · AS & A Level · Continuous random variables
Continuous random variables — practice question
Let $X$ denote a random variable whose probability density function is defined by $f(x)=\begin{cases} ax, & 0 \leq x \leq b, \\ 0, & \text{otherwise}, \end{cases}$ with $a$ and $b$ as constants.
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