Mathematics 9709 · AS & A Level · Linear combinations of random variables

Linear combinations of random variables — practice question

The random variables $X$ and $Y$ are independent, with $X \sim \mathrm{Po}(3)$ and $Y \sim \mathrm{Po}(2)$ respectively.
(a)[2]

Calculate $\mathrm{P}(2 < X < 5)$.

(b)[3]

Find the value of $\mathrm{P}(X + Y > 2)$.

(c)[4]

The total of 100 random values of $X$ and 150 random values of $Y$ is called $T$. Use an appropriate approximating distribution to find $\mathrm{P}(T < 560)$.

Worked solution & mark scheme

This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: “The working gives $e^{-3}\left(\frac{3^3}{3!}+\frac{3^4}{4!}\right)=e^{-3}(4.5+3.375)=0.22404+0.16803$.” …

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