- 3.2.1: Find the value of the constant k so thatf(x) = kx2(1 x3), 0 <x< 10,...
- 3.2.2: Let X be a continuous random variable denoting the time to failure ...
- 3.2.3: Consider a random variable X defined by the CDF:FX(x) =0, x< 0,12x ...
- 3.2.4: See Hamming [HAMM 1973]. Consider a normalized floating-point numbe...
Solutions for Chapter 3.2: The Exponential Contribution
Full solutions for Probability and Statistics with Reliability, Queuing, and Computer Science Applications | 2nd Edition
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
A study in which a sample from a population is used to make inference to a future population. Stability needs to be assumed. See Enumerative study
See Arithmetic mean.
An estimator for a parameter obtained from a Bayesian method that uses a prior distribution for the parameter along with the conditional distribution of the data given the parameter to obtain the posterior distribution of the parameter. The estimator is obtained from the posterior distribution.
Bivariate normal distribution
The joint distribution of two normal random variables
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.
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.
Coeficient of determination
See R 2 .
An experiment in which the treatments (experimental conditions) that are to be studied are included in the experiment. The data from the experiment are used to evaluate the treatments.
Conditional probability distribution
The distribution of a random variable given that the random experiment produces an outcome in an event. The given event might specify values for one or more other random variables
In hypothesis testing, this is the portion of the sample space of a test statistic that will lead to rejection of the null hypothesis.
Cumulative sum control chart (CUSUM)
A control chart in which the point plotted at time t is the sum of the measured deviations from target for all statistics up to time t
A parameter in a tabular CUSUM algorithm that is determined from a trade-off between false alarms and the detection of assignable causes.
A probability distribution for a discrete random variable
Discrete random variable
A random variable with a inite (or countably ininite) range.
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.
Fixed factor (or fixed effect).
In analysis of variance, a factor or effect is considered ixed if all the levels of interest for that factor are included in the experiment. Conclusions are then valid about this set of levels only, although when the factor is quantitative, it is customary to it a model to the data for interpolating between these levels.
Fraction defective control chart
See P chart