Mathematics 9709 · AS & A Level · The Poisson distribution

The Poisson distribution — practice question

A random variable $X$ follows the distribution $\text{Po}(2.4)$.
(a)[2]

Determine $P(2 \leq X < 4)$.

(b)[3]

Two independent values of $X$ are chosen. Determine the probability that both of these values are greater than $1$.

(c(i))[3]

It is given that $P(X = r) < P(X = r + 1)$. Determine the set of possible values of $r$.

(c(ii))[1]

Hence determine the value of $r$ for which $P(X = r)$ is greatest.

Worked solution & mark scheme

This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: Poisson expansion $e^{-2.4}\left(\dfrac{2.4^2}{2!}+\dfrac{2.4^3}{3!}\right)$

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