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# Solutions for Chapter 4.6: Independence, Conditional Probability, and the Multiplication Rule ## Full solutions for Introduction to Probability and Statistics 1 | 14th Edition

ISBN: 9781133103752 Solutions for Chapter 4.6: Independence, Conditional Probability, and the Multiplication Rule

Solutions for Chapter 4.6
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##### ISBN: 9781133103752

Since 29 problems in chapter 4.6: Independence, Conditional Probability, and the Multiplication Rule have been answered, more than 9205 students have viewed full step-by-step solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Introduction to Probability and Statistics 1, edition: 14. Chapter 4.6: Independence, Conditional Probability, and the Multiplication Rule includes 29 full step-by-step solutions. Introduction to Probability and Statistics 1 was written by and is associated to the ISBN: 9781133103752.

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

In hypothesis testing, an error incurred by rejecting a null hypothesis when it is actually true (also called a type I error).

• 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).

A formula used to determine the probability of the union of two (or more) events from the probabilities of the events and their intersection(s).

• Bayes’ theorem

An equation for a conditional probability such as PA B ( | ) in terms of the reverse conditional probability PB A ( | ).

• 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.

• Cause-and-effect diagram

A chart used to organize the various potential causes of a problem. Also called a ishbone diagram.

• Conditional probability

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

• Conditional probability density function

The probability density function of the conditional probability distribution of a continuous random variable.

• Confounding

When a factorial experiment is run in blocks and the blocks are too small to contain a complete replicate of the experiment, one can run a fraction of the replicate in each block, but this results in losing information on some effects. These effects are linked with or confounded with the blocks. In general, when two factors are varied such that their individual effects cannot be determined separately, their effects are said to be confounded.

• Contour plot

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

• Cumulative distribution function

For a random variable X, the function of X deined as PX x ( ) ? that is used to specify the probability distribution.

• Cumulative normal distribution function

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

• Defect concentration diagram

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

• Defects-per-unit control chart

See U chart

• Designed experiment

An experiment in which the tests are planned in advance and the plans usually incorporate statistical models. See Experiment

• Estimate (or point estimate)

The numerical value of a point estimator.

• 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.

• Fractional factorial experiment

A type of factorial experiment in which not all possible treatment combinations are run. This is usually done to reduce the size of an experiment with several factors.

• Gamma function

A function used in the probability density function of a gamma random variable that can be considered to extend factorials

• Geometric random variable

A discrete random variable that is the number of Bernoulli trials until a success occurs.

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