- 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 formula used to determine the probability of the union of two (or more) events from the probabilities of the events and their intersection(s).
All possible (subsets) regressions
A method of variable selection in regression that examines all possible subsets of the candidate regressor variables. Eficient computer algorithms have been developed for implementing all possible regressions
Attribute control chart
Any control chart for a discrete random variable. See Variables control chart.
A distribution with two modes
When y fx = ( ) and y is considered to be caused by x, x is sometimes called a causal variable
Any test of signiicance based on the chi-square distribution. The most common chi-square tests are (1) testing hypotheses about the variance or standard deviation of a normal distribution and (2) testing goodness of it of a theoretical distribution to sample data
Coeficient of determination
See R 2 .
An experiment in which the treatments (experimental conditions) that are to be studied are included in the experiment. The data from the experiment are used to evaluate the treatments.
In the most general usage, a measure of the interdependence among data. The concept may include more than two variables. The term is most commonly used in a narrow sense to express the relationship between quantitative variables or ranks.
Formulas used to determine the number of elements in sample spaces and events.
A subset of effects in a fractional factorial design that deine the aliases in the design.
An experiment in which the tests are planned in advance and the plans usually incorporate statistical models. See Experiment
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.
The expected value of a random variable X is its long-term average or mean value. In the continuous case, the expected value of X is E X xf x dx ( ) = ?? ( ) ? ? where f ( ) x is the density function of the random variable X.
A series of tests in which changes are made to the system under study
Finite population correction factor
A term in the formula for the variance of a hypergeometric random variable.
Fisher’s least signiicant difference (LSD) method
A series of pair-wise hypothesis tests of treatment means in an experiment to determine which means differ.
A function used in the probability density function of a gamma random variable that can be considered to extend factorials
The geometric mean of a set of n positive data values is the nth root of the product of the data values; that is, g x i n i n = ( ) = / w 1 1 .