(a)[3]
Construct the probability distribution table for $X$, writing the probabilities as numerical fractions.
(b)[3]
Calculate $\mathrm{E}(X)$ and $\mathrm{Var}(X)$.
Mathematics 9709 · AS & A Level · Discrete random variables
Discrete random variables — practice question
Becky works in an office at some times and from home at other times. The random variable $X$ represents the number of days in any one week that she works at home. It is given that $\text{P}(X = x) = kx(x + 1)$, where $k$ is a constant and $x = 1, 2, 3$ or $4$ only.
Worked solution & mark scheme
This 6-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Use $\sum$ of probabilities $=1$ to build an equation in $k$, for instance $2k+6k+12k+20k=1$.” …
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