(a(i))[2]
Show, from the diagram, that $b = 1 - a$.
(a(ii))[5]
Given that $\text{E}(X) = 1.2$, find the value of $a$.
(b)[4]
Find the value of $c$ for which $P(-c < t < c) = \frac{1}{2}$.
Mathematics 9709 · AS & A Level · Continuous random variables
Continuous random variables — practice question
The diagram is the graph of the probability density function, $f$, for a random variable $X$. It is a straight line joining $(0, a)$ to $(2, b)$, with $a$ and $b$ both positive constants. For all other values of $x$, $f(x) = 0$.
Worked solution & mark scheme
This 11-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Area condition, e.g. $\tfrac12(b-a)\times2+2a=1$ or a valid equivalent” …
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