(a)[2]
Find the constant $k$.
(b)[3]
Using this value of $k$, determine $f(x)$ for $0 \le x \le k$ and hence evaluate $\mathrm{E}(X)$.
(c)[4]
Find the value of $p$ for which $\mathrm{P}(p < X < 1) = 0.25$.
Mathematics 9709 · AS & A Level · Continuous random variables
Continuous random variables — practice question
The diagram displays the graph of the probability density function, $f$, for the random variable $X$.
Worked solution & mark scheme
This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Set up $\tfrac12\times\tfrac12 k\times k=1$ or $\int_0^k(\tfrac12 x+\tfrac12 k)\,dx=1$” …
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