- 1.10.1: Three players are each dealt, in a random manner, five cards from a...
- 1.10.2: In a certain city, three newspapers A, B, and C are published. Supp...
- 1.10.3: For the conditions of Exercise 2, what percentage of the families i...
- 1.10.4: Suppose that three compact discs are removed from their cases, and ...
- 1.10.5: Suppose that four guests check their hats when they arrive at a res...
- 1.10.6: A box contains 30 red balls, 30 white balls, and 30 blue balls. If ...
- 1.10.7: Suppose that a school band contains 10 students from the freshman c...
- 1.10.8: If n letters are placed at random in n envelopes, what is the proba...
- 1.10.9: Suppose that n letters are placed at random in n envelopes, and let...
- 1.10.10: If three letters are placed at random in three envelopes, what is t...
- 1.10.11: Suppose that 10 cards, of which five are red and five are green, ar...
- 1.10.12: Let A1, A2,... be an infinite sequence of events such that A1 A2 .....
- 1.10.13: Let A1, A2,... be an infinite sequence of events such that A1 A2 .....
Solutions for Chapter 1.10: Introduction to Probability
Full solutions for Probability and Statistics | 4th Edition
2 k p - factorial experiment
A fractional factorial experiment with k factors tested in a 2 ? p fraction with 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).
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
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.
When y fx = ( ) and y is considered to be caused by x, x is sometimes called a causal variable
The probability of an event given that the random experiment produces an outcome in another event.
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.
Cumulative normal distribution function
The cumulative distribution of the standard normal distribution, often denoted as ?( ) x and tabulated in Appendix Table II.
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.
The response variable in regression or a designed experiment.
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
Erlang random variable
A continuous random variable that is the sum of a ixed number of independent, exponential random variables.
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.
An arrangement of the frequencies of observations in a sample or population according to the values that the observations take on
A function used in the probability density function of a gamma random variable that can be considered to extend factorials
Geometric random variable
A discrete random variable that is the number of Bernoulli trials until a success occurs.
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 .