- Chapter 1: Sample Space and Probability
- Chapter 2: Discrete Random Variables
- Chapter 3: General Random Variables
- Chapter 4: Further Topics on Random Variables
- Chapter 5: Limit Theorems
- Chapter 6: The Bernoulli and Poisson Processes
- Chapter 7: Markov Chains
- Chapter 8: Bayesian Statistical Inference
- Chapter 9: Classical Statistical Inference
Introduction to Probability, 2nd Edition - Solutions by Chapter
Full solutions for Introduction to Probability, | 2nd Edition
In a fractional factorial experiment when certain factor effects cannot be estimated uniquely, they are said to be aliased.
Sequences of independent trials with only two outcomes, generally called “success” and “failure,” in which the probability of success remains constant.
Data consisting of counts or observations that can be classiied into categories. The categories may be descriptive.
A chart used to organize the various potential causes of a problem. Also called a ishbone diagram.
Central composite design (CCD)
A second-order response surface design in k variables consisting of a two-level factorial, 2k axial runs, and one or more center points. The two-level factorial portion of a CCD can be a fractional factorial design when k is large. The CCD is the most widely used design for itting a second-order model.
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.
Coeficient of determination
See R 2 .
The probability 1?a associated with a conidence interval expressing the probability that the stated interval will contain the true parameter value.
If it is possible to write a probability statement of the form PL U ( ) ? ? ? ? = ?1 where L and U are functions of only the sample data and ? is a parameter, then the interval between L and U is called a conidence interval (or a 100 1( )% ? ? conidence interval). The interpretation is that a statement that the parameter ? lies in this interval will be true 100 1( )% ? ? of the times that such a statement is made
Continuous uniform random variable
A continuous random variable with range of a inite interval and a constant probability density function.
See Control chart.
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 .
Cumulative distribution function
For a random variable X, the function of X deined as PX x ( ) ? that is used to specify the probability distribution.
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.
Another name for a probability density function
A concept in parameter estimation that uses the variances of different estimators; essentially, an estimator is more eficient than another estimator if it has smaller variance. When estimators are biased, the concept requires modiication.
A study in which a sample from a population is used to make inference to the population. See Analytic study
Error mean square
The error sum of squares divided by its number of degrees of freedom.
Estimate (or point estimate)
The numerical value of a point estimator.
A signal from a control chart when no assignable causes are present
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