Mathematics 9709 · AS & A Level · Continuous random variables

Continuous random variables — practice question

The random variable $X$ may take any value in the interval $1 \leq x \leq p$, with $p$ fixed. The diagram presents the graph of the probability density function of $X$.
(a)[2]

Show that the value of $p$ is $2$.

(b)[5]

Find the value of $\text{E}(X)$.

Worked solution & mark scheme

This 7-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Set up the area equation $\tfrac12 p(p-1)=1$.” …

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