Mathematics 9709 · AS & A Level · The Poisson distribution
The Poisson distribution — practice question
The random variables $W$ and $X$ are independent, with distributions $\text{Po}(1.2)$ and $\text{Po}(2.3)$ respectively.
(a(i))[2]
Find the value of $P(3 \leq W + X \leq 5)$.
(a(ii))[6]
The random variable $S$ is formed by adding $100$ independent values of $W$ and $200$ independent values of $X$. Use an appropriate approximation to determine $P(S > 600)$.
(b)[3]
The random variable $Y$ follows $\text{Po}(\lambda)$, where $\lambda > 0$. It is given that $\frac{5}{2} P(Y = 3) + P(Y = 4) = P(Y = 5)$. Find the value of $\lambda$ in this case.
Worked solution & mark scheme
This 11-mark question has a full step-by-step worked solution and mark scheme. One marking point: “A correct Poisson probability expression for $P(X\ge3)$, or an equivalent form” …