- 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
2 k factorial experiment.
A full factorial experiment with k factors and all factors tested at only two levels (settings) each.
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).
In hypothesis testing, a region in the sample space of the test statistic such that if the test statistic falls within it, the null hypothesis cannot be rejected. This terminology is used because rejection of H0 is always a strong conclusion and acceptance of H0 is generally a weak conclusion
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.
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.
A horizontal line on a control chart at the value that estimates the mean of the statistic plotted on the chart. See Control chart.
The tendency of data to cluster around some value. Central tendency is usually expressed by a measure of location such as the mean, median, or mode.
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.
Conditional probability density function
The probability density function of the conditional probability distribution of a continuous random variable.
The probability 1?a associated with a conidence interval expressing the probability that the stated interval will contain the true parameter value.
See Control chart.
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.
W. Edwards Deming (1900–1993) was a leader in the use of statistical quality control.
A probability distribution for a discrete random variable
Discrete uniform random variable
A discrete random variable with a inite range and constant probability mass function.
A study in which a sample from a population is used to make inference to the population. See Analytic study
Exponential random variable
A series of tests in which changes are made to the system under study
In statistical quality control, that portion of a number of units or the output of a process that is defective.
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 .