Applied Statistics and Probability for Engineers 5th 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 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

The average number of samples taken in a process monitoring or inspection scheme until the scheme signals that the process is operating at a level different from the level in which it began.

A set of rules that probabilities deined on a sample space must follow. See Probability

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

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.

A chart used to organize the various potential causes of a problem. Also called a ishbone diagram.

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

The probability mass function of the conditional probability distribution of a discrete random variable.

If it is possible to write a probability statement of the form PL U ( ) ? ? ? ? = ?1 where L and U are functions of only the sample data and ? is a parameter, then the interval between L and U is called a conidence interval (or a 100 1( )% ? ? conidence interval). The interpretation is that a statement that the parameter ? lies in this interval will be true 100 1( )% ? ? of the times that such a statement is made

An estimator that converges in probability to the true value of the estimated parameter as the sample size increases.

See Control chart.

A method to derive the probability density function of the sum of two independent random variables from an integral (or sum) of probability density (or mass) functions.

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 .

A random variable with a inite (or countably ininite) range.

A model to relate a response to one or more regressors or factors that is developed from data obtained from the system.

The numerical value of a point estimator.

The expected value of a random variable X is its long-term average or mean value. In the continuous case, the expected value of X is E X xf x dx ( ) = ?? ( ) ? ? where f ( ) x is the density function of the random variable X.

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

A discrete random variable that is the number of Bernoulli trials until a success occurs.