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# Solutions for Chapter 5.1: Bernoulli and Binomial Random Variables

## Full solutions for Fundamentals of Probability, with Stochastic Processes | 3rd Edition

ISBN: 9780131453401

Solutions for Chapter 5.1: Bernoulli and Binomial Random Variables

Solutions for Chapter 5.1
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##### ISBN: 9780131453401

Fundamentals of Probability, with Stochastic Processes was written by and is associated to the ISBN: 9780131453401. This textbook survival guide was created for the textbook: Fundamentals of Probability, with Stochastic Processes, edition: 3. This expansive textbook survival guide covers the following chapters and their solutions. Chapter 5.1: Bernoulli and Binomial Random Variables includes 34 full step-by-step solutions. Since 34 problems in chapter 5.1: Bernoulli and Binomial Random Variables have been answered, more than 15372 students have viewed full step-by-step solutions from this chapter.

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).

• Additivity property of x 2

If two independent random variables X1 and X2 are distributed as chi-square with v1 and v2 degrees of freedom, respectively, Y = + X X 1 2 is a chi-square random variable with u = + v v 1 2 degrees of freedom. This generalizes to any number of independent chi-square random variables.

• Alias

In a fractional factorial experiment when certain factor effects cannot be estimated uniquely, they are said to be aliased.

• Average run length, or ARL

The average number of samples taken in a process monitoring or inspection scheme until the scheme signals that the process is operating at a level different from the level in which it began.

• Bayesâ€™ estimator

An estimator for a parameter obtained from a Bayesian method that uses a prior distribution for the parameter along with the conditional distribution of the data given the parameter to obtain the posterior distribution of the parameter. The estimator is obtained from the posterior distribution.

• Bias

An effect that systematically distorts a statistical result or estimate, preventing it from representing the true quantity of interest.

• Conditional probability

The probability of an event given that the random experiment produces an outcome in another event.

• Control limits

See Control chart.

• 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.

• 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.

• Crossed factors

Another name for factors that are arranged in a factorial experiment.

• Cumulative sum control chart (CUSUM)

A control chart in which the point plotted at time t is the sum of the measured deviations from target for all statistics up to time t

• Decision interval

A parameter in a tabular CUSUM algorithm that is determined from a trade-off between false alarms and the detection of assignable causes.

• Demingâ€™s 14 points.

A management philosophy promoted by W. Edwards Deming that emphasizes the importance of change and quality

• Dispersion

The amount of variability exhibited by data

• Distribution function

Another name for a cumulative distribution function.

• Enumerative study

A study in which a sample from a population is used to make inference to the population. See Analytic study

• Extra sum of squares method

A method used in regression analysis to conduct a hypothesis test for the additional contribution of one or more variables to 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

• Generating function

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

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