Mathematics 9709 · AS & A Level · Linear combinations of random variables
Linear combinations of random variables — practice question
Set $A$ contains ten digits: $0, 0, 0, 0, 0, 0, 2, 2, 2, 4$. Set $B$ contains seven digits: $0, 0, 0, 0, 2, 2, 2$. A digit is selected at random from each set. The random variable $X$ is the total of the two selected digits.
(a)[2]
Show that the value of $P(X = 2)$ is $\frac{3}{7}$.
(b)[2]
Create the probability distribution table for $X$.
(c)[3]
Find the values of $\text{E}(X)$ and $\operatorname{Var}(X)$.
(d)[2]
Given that $X = 2$, find the probability that the digit selected from set $A$ was $2$.
Worked solution & mark scheme
This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Add the two relevant probabilities for $P(2)$” …