Probability and Statistics for Engineering and the Sciences

9th Edition

ISBN: 9781305251809

Author: Jay L. Devore

Publisher: Cengage Learning

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Chapter 3.5, Problem 78E

According to the article “Characterizing the Severity and Risk of Drought in the Poudre River, Colorado” (J. of Water Res. Planning and Algmnt., 2005: 383-393), the drought length Y is the number of consecutive time intervals in which the water supply remains below a critical value y₀ (a deficit), preceded by and followed by periods in which the supply exceeds this critical value (a surplus). The cited paper proposes a geometric distribution with p = .409 for this random variable.

a. What is the probability that a drought lasts exactly 3 intervals? At most 3 intervals?
b. What is the probability that the length of a drought exceeds its mean value by at least one standard deviation?

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Chapter 3 Solutions

Probability and Statistics for Engineering and the Sciences

Ch. 3.1 - A concrete beam may fail either by shear (S) or...Ch. 3.1 - Using the experiment in Example 3.3, define two...Ch. 3.1 - Let X = the number of nonzero digits in a randomly...Ch. 3.1 - If the sample space S is an infinite set, does...Ch. 3.1 - Starting at a fixed time, each car entering an...Ch. 3.1 - For each random variable defined here, describe...Ch. 3.1 - Each time a component is tested, the trial is a...Ch. 3.1 - An individual named Claudius is located at the...Ch. 3.1 - The number of pumps in use at both a six-pump...Ch. 3.2 - Let X be the number of students who show up for a...

Ch. 3.2 - Airlines sometimes overbook flights. Suppose that...Ch. 3.2 - A mail-order computer business has six telephone...Ch. 3.2 - A contractor is required by a county planning...Ch. 3.2 - Many manufacturers have quality control programs...Ch. 3.2 - Some parts of California are particularly...Ch. 3.2 - A now batterys voltage may be acceptable (A) or...Ch. 3.2 - Two fair six-sided dice are tossed independently....Ch. 3.2 - A library subscribes to two different weekly news...Ch. 3.2 - Three couples and two single individuals have been...Ch. 3.2 - Suppose that you read through this years issues of...Ch. 3.2 - Refer to Exercise 13, and calculate and graph the...Ch. 3.2 - A branch of a certain bank in New York City has...Ch. 3.2 - An insurance company offers its policyholders a...Ch. 3.2 - In Example 3.12, let Y = the number of girls born...Ch. 3.2 - Alvie Singer lives at 0 in the accompanying...Ch. 3.2 - After all students have left the classroom, a...Ch. 3.2 - Show that the cdf F(x) is a nondecreasing...Ch. 3.3 - The pmf of the amount of memory X(GB) in a...Ch. 3.3 - An individual who has automobile insurance from a...Ch. 3.3 - Refer to Exercise 12 and calculate V(Y) and Y....Ch. 3.3 - A certain brand of upright freezer is available in...Ch. 3.3 - Let X be a Bernoulli rv with pmf as in Example...Ch. 3.3 - Suppose that the number of plants of a particular...Ch. 3.3 - A small market orders copies of a certain magazine...Ch. 3.3 - Let X be the damage incurred (in ) in a certain...Ch. 3.3 - The n candidates for a job have been ranked 1, 2,...Ch. 3.3 - Possible values of X, the number of components in...Ch. 3.3 - A chemical supply company currently has in stock...Ch. 3.3 - a. Draw a line graph of the pmf of X in Exercise...Ch. 3.3 - Use the definition in Expression (3.13) to prove...Ch. 3.3 - Suppose E(X) = 5 and E[X(X - 1)] = 27.5. What is...Ch. 3.3 - Write a general rule for E(X c) where c is a...Ch. 3.3 - A result called Chebyshevs inequality states that...Ch. 3.3 - If a X b, show that a E(X) b.Ch. 3.4 - Compute the following binomial probabilities...Ch. 3.4 - The article Should You Report That Fender-Bender?...Ch. 3.4 - NBC News reported on May 2. 2013. that 1 in 20...Ch. 3.4 - A company that produces fine crystal knows from...Ch. 3.4 - A particular telephone number is used to receive...Ch. 3.4 - Refer to the previous exercise. a. What is the...Ch. 3.4 - Suppose that 30% of all students who have to buy a...Ch. 3.4 - Exercise 30 (Section 3.3) gave the pmf of Y, the...Ch. 3.4 - A particular type of tennis racket comes in a...Ch. 3.4 - Twenty percent of all telephones of a certain type...Ch. 3.4 - The College Board reports that 2% of the 2 million...Ch. 3.4 - A certain type of flashlight requires two type-D...Ch. 3.4 - A very large batch of components has arrived at a...Ch. 3.4 - An ordinance requiring that a smoke detector be...Ch. 3.4 - A toll bridge charges 1.00 for passenger cars and...Ch. 3.4 - A student who is trying to write a paper for a...Ch. 3.4 - a. For fixed n, are there values of p(0 p 1) for...Ch. 3.4 - a. Show that b(x; n, 1 p) = b(n x; n, p). b....Ch. 3.4 - Show that E(X) = np when X is a binomial random...Ch. 3.4 - Customers at a gas station pay with a credit card...Ch. 3.4 - An airport limousine can accommodate up to four...Ch. 3.4 - Refer to Chebyshevs inequality given in Exercise...Ch. 3.5 - Eighteen individuals are scheduled to take a...Ch. 3.5 - Each of 12 refrigerators of a certain type has...Ch. 3.5 - An instructor who taught two sections of...Ch. 3.5 - A geologist has collected 10 specimens of basaltic...Ch. 3.5 - A personnel director interviewing 11 senior...Ch. 3.5 - Twenty pairs of individuals playing in a bridge...Ch. 3.5 - A second-stage smog alert has been called in a...Ch. 3.5 - The probability that a randomly selected box of a...Ch. 3.5 - A family decides to have children until it has...Ch. 3.5 - Three brothers and their wives decide to have...Ch. 3.5 - According to the article Characterizing the...Ch. 3.6 - The article Expectation Analysis of the...Ch. 3.6 - Let X be the number of material anomalies...Ch. 3.6 - Suppose that the number of drivers who travel...Ch. 3.6 - Consider writing onto a computer disk and then...Ch. 3.6 - An article in the Los Angeles Times (Dec. 3. 1993)...Ch. 3.6 - The Centers for Disease Control and Prevention...Ch. 3.6 - Suppose small aircraft arrive at a certain airport...Ch. 3.6 - Organisms are present in ballast water discharged...Ch. 3.6 - The number of requests for assistance received by...Ch. 3.6 - In proof testing of circuit boards, the...Ch. 3.6 - The article Reliability-Based Service-Life...Ch. 3.6 - Let X have a Poisson distribution with parameter ....Ch. 3.6 - Suppose that trees are distributed in a forest...Ch. 3.6 - Automobiles arrive at a vehicle equipment...Ch. 3.6 - a. In a Poisson process, what has to happen in...Ch. 3 - Consider a deck consisting of seven cards, marked...Ch. 3 - After shuffling a deck of 52 cards, a dealer deals...Ch. 3 - The negative binomial rv X was defined as the...Ch. 3 - Of all customers purchasing automatic garage-door...Ch. 3 - In some applications the distribution of a...Ch. 3 - A k-out-of-n system is one that will function if...Ch. 3 - A manufacturer of integrated circuit chips wishes...Ch. 3 - Of the people passing through an airport metal...Ch. 3 - An educational consulting firm is trying to decide...Ch. 3 - Consider a disease whose presence can be...Ch. 3 - Let p1 denote the probability that any particular...Ch. 3 - The purchaser of a power-generating unit requires...Ch. 3 - A plan for an executive travelers club has been...Ch. 3 - Forty percent of seeds from maize (modern-day com)...Ch. 3 - A trial has just resulted in a hung jury because...Ch. 3 - A reservation service employs five information...Ch. 3 - Grasshoppers arc distributed at random in a large...Ch. 3 - A newsstand has ordered five copies of a certain...Ch. 3 - Individuals A and B begin to play a sequence of...Ch. 3 - A test for the presence of a certain disease has...Ch. 3 - Prob. 114SE Ch. 3 - There are two Certified Public Accountants in a...Ch. 3 - The mode of a discrete random variable X with pmf...Ch. 3 - A computer disk storage device has ten concentric...Ch. 3 - If X is a hypergeometric rv, show directly from...Ch. 3 - Prob. 119SE Ch. 3 - Prob. 120SE Ch. 3 - Prob. 121SE Ch. 3 - Prob. 122SE

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