10/2021
THE UNIVERSITY OF HONG KONG
DEPARTMENT OF STATISTICS AND ACTUARIAL SCIENCE
STAT3602 Statistical Inference
Mini-project
(assessment weighting: 15%)
Due date: 8 December, 2021
Complete both questions 1 and 2 with the help of computer software.
[Recommended: R package, downloadable from https://cran.r-project.org/bin/windows/base/.%5D
Disclaimer: The background story is entirely made-up and the data are computer-generated, although
the names are genuine. No offence.
Background
The STAT3602 class of students are the only single adults remaining in this world. They consist of
13 men and 9 women. Cupid , a matchmaking agency, offers a free trial of its new service to the class.
The service includes two parts:
Cupid will pair three men off with three women in order to maximise the satisfaction level of
the whole class.
Cupid will test for each individual whether he/she is the unanimous No. 1 choice of the opposite
sex.
Parameters
For i = 1, . . . , 13, man i has in mind three favourite women, namely woman αi,1 (most favourite),
woman αi,2 (second most favourite) and woman αi,3 (third most favourite), where αi,1, αi,2, αi,3 are
distinct integers picked from {1, 2, . . . , 9}.
Similarly, for j = 1, . . . , 9, woman j has in mind three favourite men, namely men βj,1, βj,2 and βj,3
(in descending order of priority), where βj,1, βj,2, βj,3 are distinct integers picked from {1, 2, . . . , 13}.
1
Define
θ =
