Solutions for Chapter 7: Random Variables and Probability Distributions

In hypothesis testing, an error incurred by rejecting a null hypothesis when it is actually true (also called a type I error).

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).

In statistical hypothesis testing, this is a hypothesis other than the one that is being tested. The alternative hypothesis contains feasible conditions, whereas the null hypothesis speciies conditions that are under test

The arithmetic mean of a set of numbers x1 , x2 ,…, xn is their sum divided by the number of observations, or ( / )1 1 n xi t n ? = . The arithmetic mean is usually denoted by x , and is often called the average

A qualitative characteristic of an item or unit, usually arising in quality control. For example, classifying production units as defective or nondefective results in attributes data.

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

Sequences of independent trials with only two outcomes, generally called “success” and “failure,” in which the probability of success remains constant.

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.

The mean of the conditional probability distribution of a random variable.

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.

A control chart in which the point plotted at time t is the sum of the measured deviations from target for all statistics up to time t

A parameter in a tabular CUSUM algorithm that is determined from a trade-off between false alarms and the detection of assignable causes.

See U chart

Another name for a probability density function

Another name for a cumulative distribution function.

An analysis of how the variance of the random variable that represents that output of a system depends on the variances of the inputs. A formula exists when the output is a linear function of the inputs and the formula is simpliied if the inputs are assumed to be independent.

The numerical value of a point estimator.

A type of experimental design in which every level of one factor is tested in combination with every level of another factor. In general, in a factorial experiment, all possible combinations of factor levels are tested.

A signal from a control chart when no assignable causes are present

A random variable that generalizes an Erlang random variable to noninteger values of the parameter r