(a)[2]
Find the value of $P(2 < X < 5)$.
(b)[3]
Find the value of $P(X + Y > 2)$.
(c)[4]
Let $T$ denote the sum of 100 random values of $X$ and 150 random values of $Y$. Use an appropriate approximating distribution to find $P(T < 560)$.
Mathematics 9709 · AS & A Level · The Poisson distribution
The Poisson distribution — practice question
The random variables $X$ and $Y$ are independent, with distributions $X \sim \mathrm{Po}(3)$ and $Y \sim \mathrm{Po}(2)$ respectively.
Worked solution & mark scheme
This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Using $e^{-3}\left(\frac{3^3}{3!}+\frac{3^4}{4!}\right)=e^{-3}(4.5+3.375)=0.22404+0.16803$.” …
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