A copy editor reads a $200$-page manuscript, finding $108$ typos. Suppose that the author's typos follow a Poisson process with some unknown rate $\lambda$ per page, while from long experience we know that the copyeditor finds $90\%$ of the mistakes that are there.
(a) Compute the expected number of typos found as a function of the arrival rate $\lambda$.
(b) Use the answer to (a) to find an estimate of $\lambda$ and the number of undiscovered typos.
Would appreciate some sort of push in the right direction. For part (a), I know the Expected value of a poisson is just it's rate (in this case $\lambda$). But not sure where to go from there.
Part (a): The mean number of typos found in $200$ pages will be $0.9\lambda . 200 =180\lambda$.
Part (b): We need to find a reasonable value for $\lambda$ given that an observation of a Poisson r.v. with parameter $180\lambda$ equals $108$. This gives us $\lambda = 0.6$ errors per page. This gives us an expected number of $200\lambda =120$ typos actually there, of which $12$ haven’t been found yet.