Mathematics 9709 · AS & A Level · Discrete random variables

Discrete random variables — practice question

The random variable $X$ can be $1, 2, 3, 4$. It is stated that $P(X = x) = kx(x + a)$, with $k$ and $a$ as constants.

(a)[4]

Using $P(X = 4) = 3P(X = 2)$, determine the value of $a$ and the value of $k$.

(b)[1]

Construct the probability distribution table for $X$, with the probabilities shown as numerical fractions.

(c)[2]

Given that $\text{E}(X) = 3.2$, determine $\mathrm{Var}(X)$.

Worked solution & mark scheme

This 7-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Sets up an equation from $P(X=4)=3P(X=2)$.” …