# Solutions for Chapter 5.5: Random Sums ## Full solutions for Probability and Statistics with Reliability, Queuing, and Computer Science Applications | 2nd Edition

ISBN: 9781119285427 Solutions for Chapter 5.5: Random Sums

Solutions for Chapter 5.5
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##### ISBN: 9781119285427

This textbook survival guide was created for the textbook: Probability and Statistics with Reliability, Queuing, and Computer Science Applications , edition: 2. Since 4 problems in chapter 5.5: Random Sums have been answered, more than 1585 students have viewed full step-by-step solutions from this chapter. Chapter 5.5: Random Sums includes 4 full step-by-step solutions. This expansive textbook survival guide covers the following chapters and their solutions. Probability and Statistics with Reliability, Queuing, and Computer Science Applications was written by and is associated to the ISBN: 9781119285427.

Key Statistics Terms and definitions covered in this textbook
• 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

• 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 .

• 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.

• Continuity correction.

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

• Continuous distribution

A probability distribution for a continuous random variable.

• Correction factor

A term used for the quantity ( / )( ) 1 1 2 n xi i n ? = that is subtracted from xi i n 2 ? =1 to give the corrected sum of squares deined as (/ ) ( ) 1 1 2 n xx i x i n ? = i ? . The correction factor can also be written as nx 2 .

• Correlation coeficient

A dimensionless measure of the linear association between two variables, usually lying in the interval from ?1 to +1, with zero indicating the absence of correlation (but not necessarily the independence of the two variables).

• 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.

• Degrees of freedom.

The number of independent comparisons that can be made among the elements of a sample. The term is analogous to the number of degrees of freedom for an object in a dynamic system, which is the number of independent coordinates required to determine the motion of the object.

• Density function

Another name for a probability density function

• Dependent variable

The response variable in regression or a designed experiment.

• Discrete random variable

A random variable with a inite (or countably ininite) range.

• Dispersion

The amount of variability exhibited by data

• Distribution free method(s)

Any method of inference (hypothesis testing or conidence interval construction) that does not depend on the form of the underlying distribution of the observations. Sometimes called nonparametric method(s).

• 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.

• F-test

Any test of signiicance involving the F distribution. The most common F-tests are (1) testing hypotheses about the variances or standard deviations of two independent normal distributions, (2) testing hypotheses about treatment means or variance components in the analysis of variance, and (3) testing signiicance of regression or tests on subsets of parameters in a regression model.

• False alarm

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

• Fraction defective control chart

See P chart

• Gamma function

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

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