# Solutions for Chapter 3: Discrete Probability Distributions

## Full solutions for Probability and Statistics for Engineers and Scientists | 4th Edition

ISBN: 9781111827045

Solutions for Chapter 3: Discrete Probability Distributions

Solutions for Chapter 3
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##### ISBN: 9781111827045

Since 69 problems in chapter 3: Discrete Probability Distributions have been answered, more than 5919 students have viewed full step-by-step solutions from this chapter. Chapter 3: Discrete Probability Distributions includes 69 full step-by-step solutions. This expansive textbook survival guide covers the following chapters and their solutions. Probability and Statistics for Engineers and Scientists was written by Patricia and is associated to the ISBN: 9781111827045. This textbook survival guide was created for the textbook: Probability and Statistics for Engineers and Scientists, edition: 4.

Key Statistics Terms and definitions covered in this textbook
• 2 k p - factorial experiment

A fractional factorial experiment with k factors tested in a 2 ? p fraction with all factors tested at only two levels (settings) each

• Arithmetic mean

The arithmetic mean of a set of numbers x1 , x2 ,…, xn is their sum divided by the number of observations, or ( / )1 1 n xi t n ? = . The arithmetic mean is usually denoted by x , and is often called the average

• Attribute

A qualitative characteristic of an item or unit, usually arising in quality control. For example, classifying production units as defective or nondefective results in attributes data.

• Axioms of probability

A set of rules that probabilities deined on a sample space must follow. See Probability

• Bivariate distribution

The joint probability distribution of two random variables.

• Coeficient of determination

See R 2 .

• Consistent estimator

An estimator that converges in probability to the true value of the estimated parameter as the sample size increases.

• Contour plot

A two-dimensional graphic used for a bivariate probability density function that displays curves for which the probability density function is constant.

• Correlation

In the most general usage, a measure of the interdependence among data. The concept may include more than two variables. The term is most commonly used in a narrow sense to express the relationship between quantitative variables or ranks.

• Correlation coeficient

A dimensionless measure of the linear association between two variables, usually lying in the interval from ?1 to +1, with zero indicating the absence of correlation (but not necessarily the independence of the two variables).

• Counting techniques

Formulas used to determine the number of elements in sample spaces and events.

• Critical region

In hypothesis testing, this is the portion of the sample space of a test statistic that will lead to rejection of the null hypothesis.

• Cumulative normal distribution function

The cumulative distribution of the standard normal distribution, often denoted as ?( ) x and tabulated in Appendix Table II.

• Degrees of freedom.

The number of independent comparisons that can be made among the elements of a sample. The term is analogous to the number of degrees of freedom for an object in a dynamic system, which is the number of independent coordinates required to determine the motion of the object.

• Discrete random variable

A random variable with a inite (or countably ininite) range.

• Error variance

The variance of an error term or component in a model.

• First-order model

A model that contains only irstorder terms. For example, the irst-order response surface model in two variables is y xx = + ?? ? ? 0 11 2 2 + + . A irst-order model is also called a main effects model

• Fisher’s least signiicant difference (LSD) method

A series of pair-wise hypothesis tests of treatment means in an experiment to determine which means differ.

• Fixed factor (or fixed effect).

In analysis of variance, a factor or effect is considered ixed if all the levels of interest for that factor are included in the experiment. Conclusions are then valid about this set of levels only, although when the factor is quantitative, it is customary to it a model to the data for interpolating between these levels.

• Gaussian distribution

Another name for the normal distribution, based on the strong connection of Karl F. Gauss to the normal distribution; often used in physics and electrical engineering applications

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