- Chapter 1: Probability and Counting
- Chapter 10: Inequalities and Limit Theorems
- Chapter 11: Markov Chains
- Chapter 12: Markov Chain Monte Carlo
- Chapter 13: Poisson Processes
- Chapter 2: Conditional Probability
- Chapter 3: Random Variables and their Distributions
- Chapter 4: Expectation
- Chapter 5: Continuous Random Variables
- Chapter 6: Moments
- Chapter 7: Joint Distributions
- Chapter 8: Transformations
- Chapter 9: Conditional Expectation
Introduction to Probability 1st Edition - Solutions by Chapter
Full solutions for Introduction to Probability | 1st Edition
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).
Analysis of variance (ANOVA)
A method of decomposing the total variability in a set of observations, as measured by the sum of the squares of these observations from their average, into component sums of squares that are associated with speciic deined sources of variation
Average run length, or ARL
The average number of samples taken in a process monitoring or inspection scheme until the scheme signals that the process is operating at a level different from the level in which it began.
An estimator for a parameter obtained from a Bayesian method that uses a prior distribution for the parameter along with the conditional distribution of the data given the parameter to obtain the posterior distribution of the parameter. The estimator is obtained from the posterior distribution.
An equation for a conditional probability such as PA B ( | ) in terms of the reverse conditional probability PB A ( | ).
Binomial random variable
A discrete random variable that equals the number of successes in a ixed number of Bernoulli trials.
Bivariate normal distribution
The joint distribution of two normal random variables
A horizontal line on a control chart at the value that estimates the mean of the statistic plotted on the chart. See Control chart.
Coeficient of determination
See R 2 .
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
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.
In regression, Cook’s distance is a measure of the inluence of each individual observation on the estimates of the regression model parameters. It expresses the distance that the vector of model parameter estimates with the ith observation removed lies from the vector of model parameter estimates based on all observations. Large values of Cook’s distance indicate that the observation is inluential.
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.
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.
A matrix that provides the tests that are to be conducted in an experiment.
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).
Error sum of squares
In analysis of variance, this is the portion of total variability that is due to the random component in the data. It is usually based on replication of observations at certain treatment combinations in the experiment. It is sometimes called the residual sum of squares, although this is really a better term to use only when the sum of squares is based on the remnants of a model-itting process and not on replication.
A function used in the probability density function of a gamma random variable that can be considered to extend factorials
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