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Solutions for Chapter 4.4: The Exponential and Gamma Distributions

Full solutions for Probability and Statistics for Engineering and the Sciences | 9th Edition

ISBN: 9781305251809

Solutions for Chapter 4.4: The Exponential and Gamma Distributions

Solutions for Chapter 4.4
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ISBN: 9781305251809

Chapter 4.4: The Exponential and Gamma Distributions includes 13 full step-by-step solutions. This expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Probability and Statistics for Engineering and the Sciences, edition: 9. Since 13 problems in chapter 4.4: The Exponential and Gamma Distributions have been answered, more than 89140 students have viewed full step-by-step solutions from this chapter. Probability and Statistics for Engineering and the Sciences was written by and is associated to the ISBN: 9781305251809.

Key Statistics Terms and definitions covered in this textbook
• 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.

• Alternative hypothesis

In statistical hypothesis testing, this is a hypothesis other than the one that is being tested. The alternative hypothesis contains feasible conditions, whereas the null hypothesis speciies conditions that are under test

• Biased estimator

Unbiased estimator.

• Causal variable

When y fx = ( ) and y is considered to be caused by x, x is sometimes called a causal variable

• Chi-square (or chi-squared) random variable

A continuous random variable that results from the sum of squares of independent standard normal random variables. It is a special case of a gamma random variable.

• 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 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

• Continuity correction.

A correction factor used to improve the approximation to binomial probabilities from a normal distribution.

• Correlation matrix

A square matrix that contains the correlations among a set of random variables, say, XX X 1 2 k , ,…, . The main diagonal elements of the matrix are unity and the off-diagonal elements rij are the correlations between Xi and Xj .

• 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 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

• Defect

Used in statistical quality control, a defect is a particular type of nonconformance to speciications or requirements. Sometimes defects are classiied into types, such as appearance defects and functional defects.

• Discrete uniform random variable

A discrete random variable with a inite range and constant probability mass function.

• Distribution function

Another name for a cumulative distribution function.

• Error propagation

An analysis of how the variance of the random variable that represents that output of a system depends on the variances of the inputs. A formula exists when the output is a linear function of the inputs and the formula is simpliied if the inputs are assumed to be independent.

• Estimate (or point estimate)

The numerical value of a point estimator.

• 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

• Geometric random variable

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

• 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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