- 5.8.1E: If X is a random variable with mean 33 and variance 16, use Chebysh...
- 5.8.2E: If E(X) = 17 and E(X2) = 298, use Chebyshev’s inequality to determi...
- 5.8.3E: Let X denote the outcome when a fair die is rolled. Then ? = 7/2 an...
- 5.8.4E: If the distribution of Y is b(n, 0.5), give a lower bound for P(|Y/...
- 5.8.5E: If the distribution of Y is b(n, 0.25), give a lower bound for P(|Y...
- 5.8.6E: ?Let be the mean of a random sample of size n = 15 from a distribut...
- 5.8.7E: ?Suppose that W is a continuous random variable with mean 0 and a s...
- 18.104.22.168-1: If X is a random variable with mean 33 and variance 16, use Chebysh...
- 22.214.171.124-2: If E(X) = 17 and E(X2) = 298, use Chebyshevs inequality to determin...
- 126.96.36.199-3: Let X denote the outcome when a fair die is rolled. Then = 7/2 and ...
- 188.8.131.52-4: If the distribution of Y is b(n, 0.5), give a lower bound for P(|Y/...
- 184.108.40.206-5: If the distribution of Y is b(n, 0.25), give a lower bound for P(|Y...
- 220.127.116.11-6: Let X be the mean of a random sample of size n = 15 from a distribu...
- 18.104.22.168-7: Suppose that W is a continuous random variable with mean 0 and a sy...
Solutions for Chapter 5.8: Distributions of Functions of Random Variables
Full solutions for Probability and Statistical Inference | 9th Edition
`-error (or `-risk)
In hypothesis testing, an error incurred by rejecting a null hypothesis when it is actually true (also called a type I error).
All possible (subsets) regressions
A method of variable selection in regression that examines all possible subsets of the candidate regressor variables. Eficient computer algorithms have been developed for implementing all possible regressions
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
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
The portion of the variability in a set of observations that can be traced to speciic causes, such as operators, materials, or equipment. Also called a special cause.
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.
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.
Box plot (or box and whisker plot)
A graphical display of data in which the box contains the middle 50% of the data (the interquartile range) with the median dividing it, and the whiskers extend to the smallest and largest values (or some deined lower and upper limits).
Central composite design (CCD)
A second-order response surface design in k variables consisting of a two-level factorial, 2k axial runs, and one or more center points. The two-level factorial portion of a CCD can be a fractional factorial design when k is large. The CCD is the most widely used design for itting a second-order model.
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.
When a factorial experiment is run in blocks and the blocks are too small to contain a complete replicate of the experiment, one can run a fraction of the replicate in each block, but this results in losing information on some effects. These effects are linked with or confounded with the blocks. In general, when two factors are varied such that their individual effects cannot be determined separately, their effects are said to be confounded.
Continuous uniform random variable
A continuous random variable with range of a inite interval and a constant probability density function.
In hypothesis testing, this is the portion of the sample space of a test statistic that will lead to rejection of the null hypothesis.
Used in statistical quality control, a defect is a particular type of nonconformance to speciications or requirements. Sometimes defects are classiied into types, such as appearance defects and functional defects.
Defect concentration diagram
A quality tool that graphically shows the location of defects on a part or in a process.
Another name for a probability density function
A study in which a sample from a population is used to make inference to the population. See Analytic study
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.
In statistical quality control, that portion of a number of units or the output of a process that is defective.
The geometric mean of a set of n positive data values is the nth root of the product of the data values; that is, g x i n i n = ( ) = / w 1 1 .