Question

(a) The expected number of typographical errors on any page of a certain magazine is 0.2. What

is the probability that a certain page you read contains a total of 2 or more typographical

errors? Hint: Assume that errors occur independently of each other, and the probability for

an error is small.

(b) Let N be a random number of fair coins, where N has the Poisson distribution with parameter 2. You toss each coin once. Let X be the total number of heads. Show that X P1, that is, X has the Poisson distribution with parameter λ=1.

(c) Consider a roulette wheel consisting of 38 numbers 1 through 36, 0, and 00. Smith always bets

that the outcome will be any one of the numbers 1 through 12

(1) What is the probability that Smith’s first win will occur on his fourth round?

(2) If we learn that Smith has lost all of his first four rounds, what is the probability that his

first win will occur on his seventh round?

(d) Products produced by a machine has a 4% defective rate.

(1) What is the probability that the first defective occurs in the sixth item inspected?

(2) What is the probability that the first defective occurs somewhere in the first seven in-

spections?

Pease be as much detailed as you can. Its a project question and carries alot of points. Thanks for your time and effort.

Answer 1