91Ó°ÊÓ

If \(\mathrm{X}\) follows a discrete uniform distribution, i.e. \(\mathrm{F}(\mathrm{x})=(1 / \mathrm{N})\) for \(\mathrm{x}=(1 / \mathrm{N}) 1,2, \ldots, \mathrm{N}\), find \(\mathrm{E}(\mathrm{x})\) and \(\operatorname{Var}(\mathrm{x})\).

Given that \(4 \%\) of the items in an incoming lot are defective, what is the probability that at most one defective item will be found in a random sample of size \(30 ?\) Find the Poisson approximation.

Suppose that the average number of telephone calls arriving at the switchboard of a small corporation is 30 calls per hour, (i) What is the probability that no calls will arrive in a 3 minute period? (ii) What is the probability that more than five calls will arrive in a 5 -minute interval? Assume that the number of calls arriving during any time period has a Poisson distribution.

A lot consisting of 100 fuses, is inspected by the following procedure. Five of these fuses are chosen at random and tested; if all 5 "blow" at the correct amperage, the lot is accepted. Find the probability distribution of the number of defectives in a sample of 5 assuming there are 20 in the lot.