The malicious host: a minimax solution of the Monty Hall problem

The classic solution of the Monty Hall problem tacitly assumes that, after the candidate made his/her first choice, the host always allows the candidate to switch doors after he/she showed to the candidate a losing door, not initially chosen by the candidate. In view of actual TV shows, it seems a more credible assumption that the host will or will not allow switching. Under this assumption, possible strategies for the candidate are discussed, with respect to a minimax solution of the problem. In conclusion, the classic solution does not necessarily provide a good guidance for a candidate on a game show. It is discussed that the popularity of the problem is due to its incompleteness.     

The matching, birthday and the strong birthday problem: a contemporary review

This article provides a contemporary exposition at a moderately quantitative level of the distribution theory associated with the matching and the birthday problems. A large number of examples, many not well known, are provided to help a reader have a feeling for these questions at an intuitive level.     

Locally most powerful tests for the two sample problem when the combined sample is type ii censored

We derive locally most powerful tests for the two sample problem when the combined sample is type II censored. Both middle-censored and doubly-censored cases are considered. These include, in particular, the left- and right-censored cases. The main contribution of this paper is to provide extensive small sample size tables of critical values for Wilcoxon. normal scores, Freund-Ansari-Bradley and Capon tests.     

A note on estimating the common mean of k normal distributions and the stein problem

An unbiased estimator for the common mean of k normal distributions is suggested. A necessary and sufficient condition for the estimator Lo have a smaller variance than each sample mean is given. In the case of estimating the common mean vector of k p-variate (p ≤ 3) normal distributions a combined unbiased estimator may be used. We give a class of estimators which are better than the combined estimator when the loss is quadratic and the restriction of unbiasedness is removed.     

Probability and statisitics in the service of computer science: illustrations using the assignment problem

Recent work on the assignment problem is surveyed with the aim of illustrating the contribution that stochastic thinking can make to problems of interest to computer scientists. The assignment problem is thus examined in connection with the analysis of greedy algorithms, marriage lemmas, linear programming with random costs, randomization based matching, stochastic programming, and statistical mechanics. (The survey is based on the invited presentation given during the “Statistics Days at FSU” in March 1990.)