- 3.4.1: The failure rate of a certain component is h(t) = 0t, where 0 > 0 i...
- 3.4.2: The failure rate of a computer system for onboard control of a spac...
Solutions for Chapter 3.4: Some Important Distributions
Full solutions for Probability and Statistics with Reliability, Queuing, and Computer Science Applications | 2nd Edition
Analysis of variance (ANOVA)
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
Sequences of independent trials with only two outcomes, generally called “success” and “failure,” in which the probability of success remains constant.
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 subset selected without replacement from a set used to determine the number of outcomes in events and sample spaces.
Conditional probability density function
The probability density function of the conditional probability distribution of a continuous random variable.
The probability 1?a associated with a conidence interval expressing the probability that the stated interval will contain the true parameter value.
Another term for the conidence coeficient.
An estimator that converges in probability to the true value of the estimated parameter as the sample size increases.
A two-dimensional graphic used for a bivariate probability density function that displays curves for which the probability density function is constant.
Defects-per-unit control chart
See U chart
Erlang random variable
A continuous random variable that is the sum of a ixed number of independent, exponential random variables.
The variance of an error term or component in a model.
Estimator (or point estimator)
A procedure for producing an estimate of a parameter of interest. An estimator is usually a function of only sample data values, and when these data values are available, it results in an estimate of the parameter of interest.
A subset of a sample space.
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.
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.
Geometric random variable
A discrete random variable that is the number of Bernoulli trials until a success occurs.
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 .
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