Math 6010 • Linear Models

We assume that the number of people entering a store follows a
Poisson distribution with parameter \(\lambda\). Every customer spends money in
the store, independently of each other according to a uniform distribution on
\([10,100]\). We observe \(X\), the total amount of money spent in the store on a
given day.

\textbf{(a)} Estimate \(\lambda\) using the method of moments.

\textbf{(b)} Let assume that we have the stores income
\(X_1,X_2,\ldots,X_n\) for \(n\) days and \(X_1,X_2,\ldots,X_n\) are independent and
distributed as \(X\). What would be the moment estimator for \(\lambda\) based on
\(X_1,X_2,\ldots,X_n\)?