(a(i))[1]
State the value of $\mathrm{P}(X \ge 0)$.
(a(ii))[1]
State the value of $\mathrm{P}(W \ge 0)$.
(a(iii))[1]
State an expression for $q$ in terms of $p$ only.
(b)[6]
Given that $\mathrm{E}(X)=3$, determine the value of $a$.
Mathematics 9709 · AS & A Level · Linear combinations of random variables
Linear combinations of random variables — practice question
The random variables $X$ and $W$ are assigned probability density functions $f$ and $g$, given below:
$f(x)=\begin{cases}p(a^2-x^2), & 0 \le x \le a, \\ 0, & \text{otherwise},\end{cases}$
$g(w)=\begin{cases}q(a^2-w^2), & -a \le w \le a, \\ 0, & \text{otherwise},\end{cases}$
where $a$, $p$ and $q$ are constants.