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

Linear combinations of random variables — practice question

A factory’s daily masses, in kilograms, of chemicals $A$ and $B$ are represented by the independent random variables $X$ and $Y$ respectively, where $X \sim N(10.3,\ 5.76)$ and $Y \sim N(11.4,\ 9.61)$. The revenue from the chemicals is $\$2.50$ per kilogram for $A$ and $\$3.25$ per kilogram for $B$.
(a)[2]

Find the mean and variance of the daily income earned from chemical $A$.

(b)[6]

Find the probability that, on a randomly selected day, the income from chemical $A$ exceeds the income from chemical $B$.

Worked solution & mark scheme

This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: Expected income correctly given by $E(A)=10.3\times2.50=25.75$.

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