Posted Mon 6 Oct. Due: Wed Oct 15.
Solve exercise 5.1 in the textbook. Note: they are using the term probability mass function \(f(x)\); this means, in the language of the lectures, the probability distribution function \(P(X=x)\).
A random variable \(X\) that assumes the values \(x_1, x_2,\dots,x_k\) is called a discrete uniform random variable if its probability mass function is \(f(x) = 1/k\) for all of \(x_1,x_2,\dots,x_k\) and \(0\) otherwise. Find the mean and variance of \(X\).
Solve exercise 5.6 in the textbook:
According to a survey by the Administrative Management Society, one-half of U.S. companies give employees 4 weeks of vacation after they have been with the company for 15 years. Find the probability that among 6 companies surveyed at random, the number that give employees 4 weeks of vacation after 15 years of employment is
Solve exercise 5.28 in the textbook:
A manufacturer knows that on average 20% of the electric toasters produced require repairs within 1 year after they are sold. When 20 toasters are randomly selected, find appropriate numbers x and y such that:
Solve exercise 5.36 in the textbook:
A manufacturing company uses an acceptance scheme on items from a production line before they are shipped. The plan is a two-stage one. Boxes of 25 items are readied for shipment, and a sample of 3 items is tested for defectives. If any defectives are found, the entire box is sent back for 100% screening. If no defec- tives are found, the box is shipped.
Solve exercise 5.50:
Find the probability that a person flipping a coin gets
Solve exercise 5.51:
Three people toss a fair coin and the odd one pays for coffee. If the coins all turn up the same, they are tossed again. Find the probability that fewer than 4 tosses are needed.
Solve exercise 5.101 in the textbook.
The manufacturer of a tricycle for children has received complaints about defective brakes in the product. According to the design of the product and considerable preliminary testing, it had been determined that the probability of the kind of defect in the complaint was 1 in 10,000 (i.e., 0.0001).
After a thorough investigation of the complaints, it was determined that during a certain period of time, 200 products were randomly chosen from production and 5 had defective brakes.
Comment on the “1 in 10,000” claim by the manufacturer. Use a probabilistic argument. Use the binomial distribution for your calculations.
Repeat part (a) using the Poisson approximation.
If you want to type up your homework, please don’t use Microsoft Word or the like. You can get great formatted documents in Markdown! Check out the links below.
Get familiar with professionally formatting documents using Markdown here. Want more information? Simple .md templates for PDF documents are available here.