The number of customers entering a store on a given day is a Poisson random variable with parameter \(\theta \). The money spent by a customer is uniformly distributed on \([0,\eta ]\). The number of customers and the money spent in the store are independent. We observe \(Z_1,Z_2,\ldots ,Z_n\), the total spending (the money collected by the store) on \(n\) days. We can assume that \(Z_1,Z_2,\ldots ,Z_n\) are independent.
a. Provide estimators for \(\theta \) and \(\eta \) using the method of moments. (10 points)
b. Provide estimators for \(\theta \) and \(\eta \) using the likelihood method. (10 points)