機率 Poisson random 問題
A particular typist makes an average of 0.3 typos per page.
Let X = the number of pages the proof-reader checks until
he finds the 5th pages with at least 3 typos.
- densityLv 61 decade agoFavorite Answer
First find the probability that a page has at least 3 typos:
= 1 - (probability of 0 typo + probability of 1 typo + probability of 2 typos)
= 1 - [ 0.3^0/0! + 0.3^1/1! + 0.3^2/2! ] / e^(0.3)
Let the answer be P, then the expected number of pages until you find one such page is 1/P. The expected number of pages until you find 5 such pages will be 5/P.
For further info, X follows a negative binomial distribution.
The probability that the proof-reader finds the 5th page with 3 typo on the Nth page is:
P^5 * (1-P)^(N-5) * (N-1)C(4).