Mathematics 9709 · AS & A Level · The Poisson distribution
The Poisson distribution — practice question
In a probability distribution, the random variable $X$ may take the values $-1, 0, 1, 2, 4$. The probability table for $X$ is given by $P(X=-1)=\frac{1}{4}$, $P(X=0)=p$, $P(X=1)=p$, $P(X=2)=\frac{3}{8}$, $P(X=4)=4p$.
(i)[2]
Determine the value of $p$.
(ii)[3]
Determine $\text{E}(X)$ and $\mathrm{Var}(X)$.
(iii)[2]
If $X$ is greater than zero, determine the probability that $X$ equals 2.
(c)[2]
When $X$ is greater than zero, determine the chance that $X$ takes the value $2$.
Worked solution & mark scheme
This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: “An unsimplified total of the probabilities, for example $\dfrac14 + p + p + \dfrac38 + 4p = 1$.” …