In a small town, a coffee shop offers only two menu options: coffee or tea. Over
a span of 6 months, the number of orders for each menu is recorded in the fol-
lowing table.
Month Coffee Tea
1 19 21
2 20 24
3 34 27
4 36 35
5 17 24
6 34 29
The parameter of interest is denoted by $\theta$ and represents the probability that a
given customer will order coffee. Researchers decide to use a binomial distribu-
tion to model the number of customers ordering coffee.
(a) Compute $\hat{\theta}$, the MLE of $\theta$. Write your answer rounded to the second place
after the decimal point. You have to justify your answer in the PDF file.
(b) Compute $V(\hat{\theta})$ (variance of the MLE). Write your answer rounded to the
fourth place after the decimal point.
