I'm currently preparing for my exam and in the process trying to solve some statistical problems. The question goes as follows:
Q1: A book consisting of 269 pages contains 40 missprints. Only, you don't know where the missprints are. What is the probability that a certain page contains either 0, 1 or 2 missprints? What is the average number of missprints?
Q2: In another book, also counting 269 pages, you find that by reading the first chapter consisting of 18 pages, it contains 7 missprints. What is the probability that the entire book has n missprints, where n = 7,8,...? What is the average expected missprints given the above observation?
I imagine that I have to use the following tools in a way: "Binomial distribution", "Bayes theorem", "Maximum entropi method (?)".
But I must admit that I am at a loss.
Any help would be deeply appreciated.
- Thanks!
Q1) Fix a page. The $40$ misprints can be looked at as experiments. There is a "success" if a misprint is on the fixed page and a "failure" otherwise. This means that you are dealing with binomial distribution with parameters $n=40$ and $p=\frac1{269}$.
The average number of misprints on the fixed page is the linked expectation: $np$.