- 1.7.1: Each year starts on one of the seven days (Sunday through Saturday)...
- 1.7.2: Three different classes contain 20, 18, and 25 students, respective...
- 1.7.3: In how many different ways can the five letters a, b, c, d, and e b...
- 1.7.4: If a man has six different sportshirts and four different pairs of ...
- 1.7.5: If four dice are rolled, what is the probability that each of the f...
- 1.7.6: If six dice are rolled, what is the probability that each of the si...
- 1.7.7: If 12 balls are thrown at random into 20 boxes, what is the probabi...
- 1.7.8: An elevator in a building starts with five passengers and stops at ...
- 1.7.9: Suppose that three runners from team A and three runners from team ...
- 1.7.10: A box contains 100 balls, of which r are red. Suppose that the ball...
- 1.7.11: Let n and k be positive integers such that both n and n k are large...
Solutions for Chapter 1.7: Introduction to Probability
Full solutions for Probability and Statistics | 4th 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).
In a fractional factorial experiment when certain factor effects cannot be estimated uniquely, they are said to be aliased.
See Arithmetic mean.
A method of variable selection in regression that begins with all of the candidate regressor variables in the model and eliminates the insigniicant regressors one at a time until only signiicant regressors remain
Binomial random variable
A discrete random variable that equals the number of successes in a ixed number of Bernoulli trials.
When y fx = ( ) and y is considered to be caused by x, x is sometimes called a causal variable
A horizontal line on a control chart at the value that estimates the mean of the statistic plotted on the chart. See Control chart.
Components of variance
The individual components of the total variance that are attributable to speciic sources. This usually refers to the individual variance components arising from a random or mixed model analysis of variance.
The probability of an event given that the random experiment produces an outcome in another event.
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
A tabular arrangement expressing the assignment of members of a data set according to two or more categories or classiication criteria
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.
Cumulative normal distribution function
The cumulative distribution of the standard normal distribution, often denoted as ?( ) x and tabulated in Appendix Table II.
The response variable in regression or a designed experiment.
A probability distribution for a discrete random variable
Extra sum of squares method
A method used in regression analysis to conduct a hypothesis test for the additional contribution of one or more variables to a model.
A function that is used to determine properties of the probability distribution of a random variable. See Moment-generating function
Goodness of fit
In general, the agreement of a set of observed values and a set of theoretical values that depend on some hypothesis. The term is often used in itting a theoretical distribution to a set of observations.
In multiple regression, the matrix H XXX X = ( ) ? ? -1 . This a projection matrix that maps the vector of observed response values into a vector of itted values by yˆ = = X X X X y Hy ( ) ? ? ?1 .