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Solutions for Chapter 4.5: Bivariate Distributions

Full solutions for Probability and Statistical Inference | 9th Edition

ISBN: 9780321923271

Solutions for Chapter 4.5: Bivariate Distributions

Solutions for Chapter 4.5
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ISBN: 9780321923271

This textbook survival guide was created for the textbook: Probability and Statistical Inference , edition: 9. Chapter 4.5: Bivariate Distributions includes 25 full step-by-step solutions. Since 25 problems in chapter 4.5: Bivariate Distributions have been answered, more than 93553 students have viewed full step-by-step solutions from this chapter. Probability and Statistical Inference was written by and is associated to the ISBN: 9780321923271. This expansive textbook survival guide covers the following chapters and their solutions.

Key Statistics Terms and definitions covered in this textbook
• Acceptance region

In hypothesis testing, a region in the sample space of the test statistic such that if the test statistic falls within it, the null hypothesis cannot be rejected. This terminology is used because rejection of H0 is always a strong conclusion and acceptance of H0 is generally a weak conclusion

• Attribute control chart

Any control chart for a discrete random variable. See Variables control chart.

• Bernoulli trials

Sequences of independent trials with only two outcomes, generally called “success” and “failure,” in which the probability of success remains constant.

• Bivariate normal distribution

The joint distribution of two normal 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.

• Central limit theorem

The simplest form of the central limit theorem states that the sum of n independently distributed random variables will tend to be normally distributed as n becomes large. It is a necessary and suficient condition that none of the variances of the individual random variables are large in comparison to their sum. There are more general forms of the central theorem that allow ininite variances and correlated random variables, and there is a multivariate version of the theorem.

• Combination.

A subset selected without replacement from a set used to determine the number of outcomes in events and sample spaces.

• Completely randomized design (or experiment)

A type of experimental design in which the treatments or design factors are assigned to the experimental units in a random manner. In designed experiments, a completely randomized design results from running all of the treatment combinations in random order.

• Components of variance

The individual components of the total variance that are attributable to speciic sources. This usually refers to the individual variance components arising from a random or mixed model analysis of variance.

• Conditional probability density function

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

• Conditional probability distribution

The distribution of a random variable given that the random experiment produces an outcome in an event. The given event might specify values for one or more other random variables

• 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.

• Counting techniques

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

• Curvilinear regression

An expression sometimes used for nonlinear regression models or polynomial regression models.

• Discrete distribution

A probability distribution for a discrete random variable

• Dispersion

The amount of variability exhibited by data

• Erlang random variable

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

• Estimator (or point estimator)

A procedure for producing an estimate of a parameter of interest. An estimator is usually a function of only sample data values, and when these data values are available, it results in an estimate of the parameter of interest.

• 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.

• 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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