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

Linear combinations of random variables — practice question

The distribution of the random variable $X$ is $\operatorname{Po}(1.5)$.
(a)[2]

Determine $P(X \geq 3)$.

(b)[3]

Find the probability that the total of three independent values of $X$ lies between $3$ and $5$ inclusive.

(c)[5]

A large number, $n$, of values of $X$ are added together and the total is called $T$. Using a suitable approximation, it was found that $P(T > 330) = 0.0391$, correct to $3$ significant figures. Determine the value of $n$.

Worked solution & mark scheme

This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Substitute $1-e^{-1.5}(1+1.5+\tfrac{1.5^2}{2})$” …

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