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

Linear combinations of random variables — practice question

The random variable $X$ follows a normal distribution with mean 10 and standard deviation 3, while the independent random variable $Y$ follows a Poisson distribution with mean 4.
(a)[3]

Find the standard deviation for $X + Y$.

(b)[3]

Find the standard deviation for $5X - Y$.

Worked solution & mark scheme

This 6-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Hence $\operatorname{Var}(Y)=4$” …

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