- 4.8.1: A person arrives at a certain bus stop each morning. The waiting ti...
- 4.8.2: Resistors are labeled 100 . In fact, the actual resistances are uni...
- 4.8.3: Let T (4, 0.5). a. Find T . b. Find T . c. Find P(T 1). d. Find P(T...
- 4.8.4: Let T (r, ). If T = 8 and 2 T = 16, find r and
- 4.8.5: Let T (r, ). If T = 8 and r = 16, find and 2 .
- 4.8.6: The lifetime, in years, of a type of small electric motor operating...
- 4.8.7: Let T Weibull(0.5, 3). a. Find T . b. Find T . c. Find P(T < 1). d....
- 4.8.8: If T is a continuous random variable that is always positive (such ...
- 4.8.9: In the article Parameter Estimation with Only One Complete Failure ...
- 4.8.10: The lifetime of a certain battery is modeled with the Weibull distr...
- 4.8.11: The lifetime of a cooling fan, in hours, that is used in a computer...
- 4.8.12: Someone suggests that the lifetime T (in days) of a certain compone...
- 4.8.13: A system consists of two components connected in series. The system...
- 4.8.14: Let X U(a, b). Use the definition of the mean of a continuous rando...
- 4.8.15: Let X U(a, b). Use the definition of the variance of a continuous r...
- 4.8.16: Let X U(a, b). a. Show that if x a then P(X x) = 0. b. Show that if...
- 4.8.17: Let U U(0, 1). Let a and b be constants with a < b, and let X = (b ...
Solutions for Chapter 4.8: Some Other Continuous Distributions
Full solutions for Statistics for Engineers and Scientists | 4th 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
Average run length, or ARL
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.
When y fx = ( ) and y is considered to be caused by x, x is sometimes called a causal variable
Central limit theorem
The simplest form of the central limit theorem states that the sum of n independently distributed random variables will tend to be normally distributed as n becomes large. It is a necessary and suficient condition that none of the variances of the individual random variables are large in comparison to their sum. There are more general forms of the central theorem that allow ininite variances and correlated random variables, and there is a multivariate version of the theorem.
The portion of the variability in a set of observations that is due to only random forces and which cannot be traced to speciic sources, such as operators, materials, or equipment. Also called a common cause.
Conditional probability density function
The probability density function of the conditional probability distribution of a continuous random variable.
A correction factor used to improve the approximation to binomial probabilities from a normal distribution.
A two-dimensional graphic used for a bivariate probability density function that displays curves for which the probability density function is constant.
See Control chart.
A dimensionless measure of the linear association between two variables, usually lying in the interval from ?1 to +1, with zero indicating the absence of correlation (but not necessarily the independence of the two variables).
A square matrix that contains the correlations among a set of random variables, say, XX X 1 2 k , ,…, . The main diagonal elements of the matrix are unity and the off-diagonal elements rij are the correlations between Xi and Xj .
A square matrix that contains the variances and covariances among a set of random variables, say, X1 , X X 2 k , , … . The main diagonal elements of the matrix are the variances of the random variables and the off-diagonal elements are the covariances between Xi and Xj . Also called the variance-covariance matrix. When the random variables are standardized to have unit variances, the covariance matrix becomes the correlation matrix.
An expression sometimes used for nonlinear regression models or polynomial regression models.
Defects-per-unit control chart
See U chart
A study in which a sample from a population is used to make inference to the population. See Analytic study
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
In statistical quality control, that portion of a number of units or the output of a process that is defective.
A function used in the probability density function of a gamma random variable that can be considered to extend factorials
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