MATH235 Week 8 - Workshop problems

A random survey of 3 members of a philosophy department (total size 6) reported that none are in favour of hanging. Let $n$ denote the (unknown) number in favour in the whole department. Write down the probability of this survey observation conditional on an arbitrary value of $n$. Write down the likelihood function of $n$. Compare this function with that obtained had all 3 members of the sample had been in favour.

A small call centre that I regularly have occasion to contact has $k$ employees that answer the telephones.

1. (a)

   I contact the call centre on three separate occasions. On the first occasion, my call is taken by Anna, the second occasion by Brian and the third occasion by Anna again. Write down the likelihood of $k$, and hence calculate the MLE of $k$.

2. (b)

   I contact the call centre a fourth time, and the phone is answered by Clare. Write down the new likelihood, and hence calculate the revised MLE of $k$ in light of the new information.