Probability and Statistics for Engineering and the Sciences

9th Edition

ISBN: 9781305251809

Author: Jay L. Devore

Publisher: Cengage Learning

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Correlation

Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.

Linear Correlation

A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.

Regression Analysis

Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as p…

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Textbook Question

Chapter 4.5, Problem 79E

Nonpoint source loads are chemical masses that travel to the main stem of a river and its tributaries in flows that are distributed over relatively long stream reaches, in contrast to those that enter at well-defined and regulated points. The article “Assessing Uncertainty in Mass Balance Calculation of River Nonpoint Source Loads” (J. of Envir. Engr., 2008: 247–258) suggested that for a certain time period and location, X 5 nonpoint source load of total dissolved solids could be modeled with a lognormal distribution having mean value 10,281 kg/day/km and a coefficient of variation C V = .40 ( C V = σ X / μ X ) .

a. What are the mean value and standard deviation of ln(X)?

b. What is the probability that X is at most 15,000 kg/day/km?

c. What is the probability that X exceeds its mean value, and why is this probability not .5?

d. Is 17,000 the 95th percentile of the distribution?

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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Chapter 4 Solutions

Probability and Statistics for Engineering and the Sciences

Ch. 4.1 - The current in a certain circuit as measured by an...Ch. 4.1 - Suppose the reaction temperature X (in C) in a...Ch. 4.1 - The error involved in making a certain measurement...Ch. 4.1 - Let X denote the vibratory stress (psi) on a wind...Ch. 4.1 - A college professor never finishes his lecture...Ch. 4.1 - The actual tracking weight of a stereo cartridge...Ch. 4.1 - The article Second Moment Reliability Evaluation...Ch. 4.1 - Prob. 8E Ch. 4.1 - Based on an analysis of sample data, the article...Ch. 4.1 - A family of pdfs that has been used to approximate...

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