Mathematics 9709 · AS & A Level · Linear combinations of random variables
Linear combinations of random variables — practice question
A fair die has faces marked $1, 1, 2, 2, 3, 3$. Let the random variable $W$ denote the score on one throw, namely the number showing on the top face after the die comes to rest.
(i)[3]
Determine the mean and standard deviation of $W$.
(ii)[4]
The die is tossed twice and the random variable $X$ is the total of the two scores. Set out a probability distribution table for $X$.
(iii)[3]
The die is thrown $n$ times, and the random variable $Y$ represents the number of times that the score is 3. If $\text{E}(Y) = 8$, find $\mathrm{Var}(Y)$.
Worked solution & mark scheme
This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Finds mean $=\frac{11}{6}$.” …