Mathematics 9709 · AS & A Level · The Poisson distribution

The Poisson distribution — practice question

The random variable $X$ follows the distribution $\text{Po}(\lambda)$.
(a(i))[1]

State the values that are possible for $X$.

(a(ii))[1]

You are told that $P(X = 1) = 3 \times P(X = 0)$. Determine $\lambda$.

(a(iii))[2]

Calculate $P(4 \le X \le 6)$.

(b)[5]

The random variable $Y$ follows the distribution $\text{Po}(\mu)$, with $\mu$ large. Using an appropriate approximating distribution, it is found that $P(Y < 46) = 0.0668$, correct to $4$ decimal places. Find $\mu$.

Worked solution & mark scheme

This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: Support identified correctly as $0,1,2,3,\ldots$

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