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State the value of $\text{E}(X)$ and demonstrate that $\mathrm{Var}(X)=\frac{9}{5}$.
Mathematics 9709 · AS & A Level · Continuous random variables
Continuous random variables — practice question
The probability density function, $f$, for the random variable $X$ is defined as
$f(x) = \begin{cases} k(6x - x^2), & 0 \leq x \leq 6, \\ 0, & \text{otherwise}, \end{cases}$
with $k$ as a constant.