(i)[3]
Construct the probability distribution table for $X$, in terms of $k$, and determine the value of $k$.
(ii)[3]
Find the values of $\mathrm{E}(X)$ and $\mathrm{Var}(X)$.
Mathematics 9709 · AS & A Level · The Poisson distribution
The Poisson distribution — practice question
The random variable $X$ can only have the values $-1, 1, 2, 3$. The probability that $X$ takes the value $x$ is $kx^2$, 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: “Probability distribution table showing the correct $x$-values and probabilities written in terms of $k$” …
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