- 0.0.1: In each of the following situations, indicate whether f = O(g), or ...
- 0.0.2: Show that, if c is a positive real number, then g(n) = 1 + c + c2 +...
- 0.0.3: The Fibonacci numbers F0, F1, F2, . . . , are defined by the ruleF0...
- 0.0.4: Is there a faster way to compute the nth Fibonacci number than by f...
Solutions for Chapter 0: Prologue
Full solutions for Algorithms | 1st Edition
Adjusted R 2
A variation of the R 2 statistic that compensates for the number of parameters in a regression model. Essentially, the adjustment is a penalty for increasing the number of parameters in the model. Alias. In a fractional factorial experiment when certain factor effects cannot be estimated uniquely, they are said to be aliased.
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
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.
A distribution with two modes
The joint probability distribution of two random variables.
An attribute control chart that plots the total number of defects per unit in a subgroup. Similar to a defects-per-unit or U chart.
Data consisting of counts or observations that can be classiied into categories. The categories may be descriptive.
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.
Conditional probability mass function
The probability mass function of the conditional probability distribution of a discrete random variable.
The probability 1?a associated with a conidence interval expressing the probability that the stated interval will contain the true parameter value.
A graphical display used to monitor a process. It usually consists of a horizontal center line corresponding to the in-control value of the parameter that is being monitored and lower and upper control limits. The control limits are determined by statistical criteria and are not arbitrary, nor are they related to speciication limits. If sample points fall within the control limits, the process is said to be in-control, or free from assignable causes. Points beyond the control limits indicate an out-of-control process; that is, assignable causes are likely present. This signals the need to ind and remove the assignable causes.
A term used for the quantity ( / )( ) 1 1 2 n xi i n ? = that is subtracted from xi i n 2 ? =1 to give the corrected sum of squares deined as (/ ) ( ) 1 1 2 n xx i x i n ? = i ? . The correction factor can also be written as nx 2 .
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.
W. Edwards Deming (1900–1993) was a leader in the use of statistical quality control.
Another name for a probability density function
A property of a collection of events that indicates that their union equals the sample space.
Fixed factor (or fixed effect).
In analysis of variance, a factor or effect is considered ixed if all the levels of interest for that factor are included in the experiment. Conclusions are then valid about this set of levels only, although when the factor is quantitative, it is customary to it a model to the data for interpolating between these levels.
In statistical quality control, that portion of a number of units or the output of a process that is defective.
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.