The following data give the numbers of occupants in 1768 cars observed on a road junction in Jakarta, Indonesia, during a certain time period on a weekday morning. The proposed model for number of...

The following data give the numbers of occupants in 1768 cars observed on a road junction in Jakarta, Indonesia, during a certain time period on a weekday morning.

The proposed model for number of occupants X is truncated Poisson (TP), defined as

(i) Write down the likelihood (or the log-likelihood) function. Is it straightforward to find the MLE of λ by maximizing the likelihood or log-likelihood directly?

(ii) Develop an EM algorithm for approximating the MLE of λ. Hznt: Assume that missing data is io - the number of cases when X = 0. so with the complete data the model is Poisson.
(λ). Estimate X from the complete data. Update io given the estimator of λ.

(iii) Write MATLAB program that will estimate the MLE of λ for Jakarta cars data using the EN procedure from (ii).