(a)[2]
Construct the probability distribution table for $X$, in terms of $k$.
(b)[4]
Demonstrate that $\operatorname{Var}(X) = 1.05$.
Mathematics 9709 · AS & A Level · Discrete random variables
Discrete random variables — practice question
The random variable $X$ can take only the values 1, 2, 3, 4. The probability that $X$ has the value $x$ is $kx(5-x)$, where $k$ is a constant.
Worked solution & mark scheme
This 6-mark question has a full step-by-step worked solution and mark scheme. One marking point: “At least one probability correctly expressed in terms of $k$, for example $P(X=1)=4k$” …
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