(a)[5]
Find the mean and standard deviation for $X - 3Y$.
(b)[3]
Find the value of $P(Y = 15X)$.
Mathematics 9709 · AS & A Level · Linear combinations of random variables
Linear combinations of random variables — practice question
The independent random variables $X$ and $Y$ are distributed as $\text{Po}(2)$ and $\text{B}(20, \tfrac{1}{4})$ respectively.
Worked solution & mark scheme
This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Obtains $\text{E}(Y)=\frac{20}{4}=5$ and $\mathrm{Var}(Y)=20\times\frac14\times\frac34=\frac{15}{4}$” …
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