- 16.16.1: Refer to the results of Example 16.2 given in Table 16.1. a Which o...
- 16.16.2: Define each of the following: a Prior distribution for a parameter ...
- 16.16.3: Applet Exercise The applet Binomial Revision can be used to explore...
- 16.16.4: Applet Exercise Scroll down to the section Applet with Controls on ...
- 16.16.5: Repeat the directions in Exercise 16.4, using a beta prior with = 1...
- 16.16.6: Suppose that Y is a binomial random variable based on n trials and ...
- 16.16.7: In Section 16.1 and Exercise 16.6, we considered an example where t...
- 16.16.8: Refer to Exercise 16.6. If Y is a binomial random variable based on...
- 16.16.9: Suppose that we conduct independent Bernoulli trials and record Y ,...
- 16.16.11: Let Y1, Y2,..., Yn denote a random sample from a Poisson-distribute...
- 16.16.12: Let Y1, Y2,..., Yn denote a random sample from a normal population ...
- 16.16.13: Applet Exercise Activate the applet Binomial Revision and scroll do...
- 16.16.14: Applet Exercise Refer to Exercise 16.13. Select a value for the tru...
- 16.16.15: Applet Exercise In Exercise 16.7, we reconsidered our introductory ...
- 16.16.16: Applet Exercise Repeat the instructions for Exercise 16.15, assumin...
- 16.16.17: Applet Exercise In Exercise 16.9, we used a beta prior with paramet...
- 16.16.18: Applet Exercise In Exercise 16.10, we found the posterior density f...
- 16.16.19: Applet Exercise In Exercise 16.11, we found the posterior density f...
- 16.16.21: Applet Exercise In Exercise 16.15, we determined that the posterior...
- 16.16.22: Applet Exercise Exercise 16.16 used different prior parameters but ...
- 16.16.23: Applet Exercise In Exercise 16.17, we obtained a beta posterior wit...
- 16.16.24: Applet Exercise In Exercise 16.18, we found the posterior density f...
- 16.16.25: Applet Exercise In Exercise 16.19, we found the posterior density f...
- 16.16.26: Applet Exercise In Exercise 16.20, we determined the posterior of v...
Solutions for Chapter 16: Introduction to Bayesian Methods for Inference
Full solutions for Mathematical Statistics with Applications | 7th Edition
The arithmetic mean of a set of numbers x1 , x2 ,…, xn is their sum divided by the number of observations, or ( / )1 1 n xi t n ? = . The arithmetic mean is usually denoted by x , and is often called the average
A distribution with two modes
Binomial random variable
A discrete random variable that equals the number of successes in a ixed number of Bernoulli trials.
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.
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).
A horizontal line on a control chart at the value that estimates the mean of the statistic plotted on the chart. See Control chart.
Chi-square (or chi-squared) random variable
A continuous random variable that results from the sum of squares of independent standard normal random variables. It is a special case of a gamma random variable.
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.
An estimator that converges in probability to the true value of the estimated parameter as the sample size increases.
A measure of association between two random variables obtained as the expected value of the product of the two random variables around their means; that is, Cov(X Y, ) [( )( )] =? ? E X Y ? ? X Y .
The value of a statistic corresponding to a stated signiicance level as determined from the sampling distribution. For example, if PZ z PZ ( )( .) . ? =? = 0 025 . 1 96 0 025, then z0 025 . = 1 9. 6 is the critical value of z at the 0.025 level of signiicance. Crossed factors. Another name for factors that are arranged in a factorial experiment.
A parameter in a tabular CUSUM algorithm that is determined from a trade-off between false alarms and the detection of assignable causes.
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.
Degrees of freedom.
The number of independent comparisons that can be made among the elements of a sample. The term is analogous to the number of degrees of freedom for an object in a dynamic system, which is the number of independent coordinates required to determine the motion of the object.
Error of estimation
The difference between an estimated value and the true value.
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
Gamma random variable
A random variable that generalizes an Erlang random variable to noninteger values of the parameter r
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