(a)[1]
State the value obtained for $\text{E}(X)$.
(b)[3]
Find the value of $\text{Var}(X)$.
(c)[5]
From two worms of this type chosen at random, find the probability that exactly one has length less than $6\text{ cm}$.
Mathematics 9709 · AS & A Level · Continuous random variables
Continuous random variables — practice question
The random variable $X$, measured in centimetres and representing the length of worms of a certain type, is modelled by the probability density function
$f(x) = \begin{cases} \frac{6}{125}(10 - x)(x - 5), & 5 \le x \le 10, \\ 0, & \text{otherwise}. \end{cases}$