# Solutions for Chapter 5-1: Discrete Probability Distributions

## Full solutions for Elementary Statistics: A Step by Step Approach | 7th Edition

ISBN: 9780073534978

Solutions for Chapter 5-1: Discrete Probability Distributions

Solutions for Chapter 5-1
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##### ISBN: 9780073534978

Elementary Statistics: A Step by Step Approach was written by and is associated to the ISBN: 9780073534978. This expansive textbook survival guide covers the following chapters and their solutions. Since 36 problems in chapter 5-1: Discrete Probability Distributions have been answered, more than 13127 students have viewed full step-by-step solutions from this chapter. This textbook survival guide was created for the textbook: Elementary Statistics: A Step by Step Approach, edition: 7. Chapter 5-1: Discrete Probability Distributions includes 36 full step-by-step solutions.

Key Statistics Terms and definitions covered in this textbook
• a-error (or a-risk)

In hypothesis testing, an error incurred by failing to reject a null hypothesis when it is actually false (also called a type II error).

• 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

• Assignable cause

The portion of the variability in a set of observations that can be traced to speciic causes, such as operators, materials, or equipment. Also called a special cause.

• 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.

• Bivariate distribution

The joint probability distribution of two random variables.

• Block

In experimental design, a group of experimental units or material that is relatively homogeneous. The purpose of dividing experimental units into blocks is to produce an experimental design wherein variability within blocks is smaller than variability between blocks. This allows the factors of interest to be compared in an environment that has less variability than in an unblocked experiment.

• Coeficient of determination

See R 2 .

• Convolution

A method to derive the probability density function of the sum of two independent random variables from an integral (or sum) of probability density (or mass) functions.

• Covariance matrix

A square matrix that contains the variances and covariances among a set of random variables, say, X1 , X X 2 k , , … . The main diagonal elements of the matrix are the variances of the random variables and the off-diagonal elements are the covariances between Xi and Xj . Also called the variance-covariance matrix. When the random variables are standardized to have unit variances, the covariance matrix becomes the correlation matrix.

• Defect concentration diagram

A quality tool that graphically shows the location of defects on a part or in a process.

• Erlang random variable

A continuous random variable that is the sum of a ixed number of independent, exponential random variables.

• Error variance

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

• Expected value

The expected value of a random variable X is its long-term average or mean value. In the continuous case, the expected value of X is E X xf x dx ( ) = ?? ( ) ? ? where f ( ) x is the density function of the random variable X.

• Exponential random variable

A series of tests in which changes are made to the system under study

• Factorial experiment

A type of experimental design in which every level of one factor is tested in combination with every level of another factor. In general, in a factorial experiment, all possible combinations of factor levels are tested.

• False alarm

A signal from a control chart when no assignable causes are present

• Fraction defective

In statistical quality control, that portion of a number of units or the output of a process that is defective.

• Fraction defective control chart

See P chart

• Generating function

A function that is used to determine properties of the probability distribution of a random variable. See Moment-generating function

• Harmonic mean

The harmonic mean of a set of data values is the reciprocal of the arithmetic mean of the reciprocals of the data values; that is, h n x i n i = ? ? ? ? ? = ? ? 1 1 1 1 g .

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