Probability and Statistics for Engineers and Scientists 4th Edition - Solutions by Chapter

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.

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.

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

A distribution with two modes

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.

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.

A type of experimental design in which the treatments or design factors are assigned to the experimental units in a random manner. In designed experiments, a completely randomized design results from running all of the treatment combinations in random order.

A continuous random variable with range of a inite interval and a constant probability density function.

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.

For a random variable X, the function of X deined as PX x ( ) ? that is used to specify the probability distribution.

A quality tool that graphically shows the location of defects on a part or in a process.

See U chart

Another name for a probability density function

A continuous random variable that is the sum of a ixed number of independent, exponential random variables.

The difference between an estimated value and the true value.

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.

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

Another name for the normal distribution, based on the strong connection of Karl F. Gauss to the normal distribution; often used in physics and electrical engineering applications