Suppose that the number of printing mistakes on each page of a200-page Mathematics book is independent of that on other pages.and it follows a Poisson distribution with mean 0.2.
(a) Find the probability that there is no printing mistake onpage 23.
(b) Let page N be the first page which contains printingmistakes.
Find (i) the probability that N is less than or equal to 3,
(ii) the mean and variance of N.
(c) Let M be the number of pages which contain printingmistakes.Find the mean and variance of M.
(d) Suppose there is another 200-page Statistics book and thereare 40 printing mistakes randomly and independently scatteredthrough it.
Let Y be the number of printing mistakes on page 23.
(i) Which of the distributions - Bernoulli, binomial, geometric,Poisson, does Y follow?
(ii) Find the probability that there is no printing mistake onpage 23.
