(a)[1]
The random variable $W$ follows a Poisson distribution. State the relationship between $\mathrm{E}(W)$ and $\mathrm{Var}(W)$.
(b)[1]
The random variable $X$ has distribution $\mathrm{B}(n, p)$. Jyothi wants to use a Poisson distribution as an approximate model for $X$. Using the formulae for $\mathrm{E}(X)$ and $\mathrm{Var}(X)$, explain why $p$ has to be near $0$ for this approximation to be reasonable.
(c)[3]
For $Y$ with distribution $\mathrm{B}(20000, 0.00007)$, use a Poisson distribution to estimate $\mathrm{P}(Y > 2)$.