 9.43E: Let Y1, Y2, . . . , Yn denote independent and identically distribut...
 9.1E: In Exercise 8.8, we considered a random sample of size 3 from an ex...
 9.2E: Let Y1, Y2, . . . , Yn denote a random sample from a population wit...
 9.3E: Let Y1, Y2, . . . , Yn denote a random sample from the uniform dist...
 9.4E: ReferenceLet Y1, Y2, . . . , Yn denote a random sample of size n fr...
 9.5E: Suppose that Y1, Y2, . . . , Yn is a random sample from a normal di...
 9.6E:
 9.7E: Suppose that Y1, Y2, . . . , Yn denote a random sample of size n fr...
 9.8E: Let Y1, Y2, . . . , Yn denote a random sample from a probability de...
 9.9E: Applet Exercise How was Figure 9.1 obtained? Access the applet Poin...
 9.10E: Applet Exercise Refer to Exercise 9.9. Scroll down to the portion o...
 9.11E: Applet Exercise Refer to Exercises 9.9 and 9.10. How can the result...
 9.12E: Applet Exercise Refer to Exercise 9.11. What happens if each sequen...
 9.13E: Applet Exercise Refer to Exercises 9.9–9.12. Access the applet Poin...
 9.14E: Applet Exercise Refer to Exercise 9.13. Scroll down to the portion ...
 9.15E: Refer to Exercise 9.3. Show that both are consistent estimators for...
 9.16E: Refer to Exercise 9.5. Is a consistent estimator of ? 2?Reference
 9.17E:
 9.18E: In Exercise 9.17, suppose that the populations are normally distrib...
 9.19E: Let Y1, Y2, . . . , Yn denote a random sample from the probability ...
 9.20E: If Y has a binomial distribution with n trials and success probabil...
 9.21E: Let Y1, Y2, . . . , Yn be a random sample of size n from a normal p...
 9.22E: Refer to Exercise 9.21. Suppose that Y1, Y2, . . . , Yn is a random...
 9.23E: that n = 2k for some integer k. Consider ReferenceLet Y1, Y2, . . ....
 9.24E: Let Y1, Y2, Y3, . . . Yn be independent standard normal random vari...
 9.25E: Suppose that Y1, Y2, . . . , Yn denote a random sample of size n fr...
 9.26E: It is sometimes relatively easy to establish consistency or lack of...
 9.27E: Use the method described in Exercise 9.26 to show that, if Y(1) = m...
 9.28E: Let Y1, Y2, . . . , Yn denote a random sample of size n from a Pare...
 9.29E: Let Y1, Y2, . . . , Yn denote a random sample of size n from a powe...
 9.30E: Let Y1, Y2, . . . , Yn be independent random variables, each with p...
 9.31E: If Y1, Y2, . . . , Yn denote a random sample from a gamma distribut...
 9.32E: Let Y1, Y2, . . . , Yn denote a random sample from the probability ...
 9.33E: An experimenter wishes to compare the numbers of bacteria of types ...
 9.34E: The Rayleigh density function is given by ReferenceA density functi...
 9.35E: Let Y1, Y2, . . . be a sequence of random variables with Notice tha...
 9.36E: Suppose that Y has a binomial distribution based on n trials and su...
 9.37E: Let X1, X2, . . . , Xn denote n independent and identically distrib...
 9.38E: Let Y1 , Y2, . . . , Yn denote a random sample from a normal distri...
 9.39E: Let Y1, Y2, . . . , Yn denote a random sample from a Poisson distri...
 9.40E: Let Y1, Y2, . . . , Yn denote a random sample from a Rayleigh distr...
 9.41E: Let Y1, Y2, . . . , Yn denote a random sample from a Weibull distri...
 9.42E: If Y1, Y2, . . . , Yn denote a random sample from a geometric distr...
 9.44E: Let Y1, Y2, . . . , Yn denote independent and identically distribut...
 9.45E: Suppose that Y1, Y2, . . . , Yn is a random sample from a probabili...
 9.46E: If Y1, Y2, . . . , Yn denote a random sample from an exponential di...
 9.47E: Refer to Exercise 9.43. If ? is known, show that the power family o...
 9.48E: Refer to Exercise 9.44. If ? is known, show that the Pareto distrib...
 9.49E: Let Y1, Y2, . . . , Yn denote a random sample from the uniform dist...
 9.50E: Let Y1, Y2, . . . , Yn denote a random sample from the uniform dist...
 9.51E: Let Y1, Y2, . . . , Yn denote a random sample from the probability ...
 9.52E: Let Y1, Y2, . . . , Yn be a random sample from a population with de...
 9.53E: Let Y1, Y2, . . . , Yn be a random sample from a population with de...
 9.54E: Let Y1, Y2, . . . , Yn denote independent and identically distribut...
 9.55E: Let Y1, Y2, . . . , Yn denote independent and identically distribut...
 9.56E: Refer to Exercise 9.38(b). Find an MVUE of ? 2.Reference
 9.57E: Refer to Exercise 9.18. Is the estimator of ? 2 given there an MVUE...
 9.58E: Refer to Exercise 9.40. Use to find an MVUE of ? .Reference
 9.59E: The number of breakdowns Y per day for a certain machine is a Poiss...
 9.60E: Reference
 9.61E: Refer to Exercise 9.49. Use Y(n) to find an MVUE of ?. (See Example...
 9.62E: Refer to Exercise 9.51. Find a function of Y(1) that is an MVUE for...
 9.63E: Let Y1, Y2, . . . , Yn be a random sample from a population with de...
 9.64E: Let Y1, Y2, . . . , Yn be a random sample from a normal distributio...
 9.65E: In this exercise, we illustrate the direct use of the Rao–Blackwell...
 9.66E: The likelihood function L(y1, y2, . . . , yn  ?) takes on differen...
 9.67E: Refer to Exercise 9.66. Suppose that a sample of size n is taken fr...
 9.68E: Suppose that a statistic U has a probability density function that ...
 9.69E: Let Y1, Y2, . . . , Yn denote a random sample from the probability ...
 9.70E: Suppose that Y1, Y2, . . . , Yn constitute a random sample from a P...
 9.71E: If Y1, Y2, . . . , Yn denote a random sample from the normal distri...
 9.72E: If Y1, Y2, . . . , Yn denote a random sample from the normal distri...
 9.73E: An urn contains ? black balls and N ? ? white balls. A sample of n ...
 9.74E: Let Y1, Y2, . . . , Yn constitute a random sample from the probabil...
 9.75E: Let Y1, Y2, . . . , Yn be a random sample from the probability dens...
 9.76E: Let X1, X2, X3, . . . be independent Bernoulli random variables suc...
 9.77E: Let Y1, Y2, . . . , Yn denote independent and identically distribut...
 9.78E: Let Y1, Y2, . . . , Yn denote independent and identically distribut...
 9.79E: Let Y1, Y2, . . . , Yn denote independent and identically distribut...
 9.80E: Suppose that Y1, Y2, . . . , Yn denote a random sample from the Poi...
 9.81E: Suppose that Y1, Y2, . . . , Yn denote a random sample from an expo...
 9.82E: Let Y1, Y2, . . . , Yn denote a random sample from the density func...
 9.83E: Suppose that Y1, Y2, . . . , Yn constitute a random sample from a u...
 9.84E: A certain type of electronic component has a lifetime Y (in hours) ...
 9.85E: Let Y1, Y2, . . . , Yn denote a random sample from the density func...
 9.86E: Suppose that X1, X2, . . . , Xm, representing yields per acre for c...
 9.87E: A random sample of 100 voters selected from a large population reve...
 9.88E: Let Y1, Y2, . . . , Yn denote a random sample from the probability ...
 9.89E: It is known that the probability p of tossing heads on an unbalance...
 9.90E: A random sample of 100 men produced a total of 25 who favored a con...
 9.91E: Find the MLE of ? based on a random sample of size n from a uniform...
 9.92E: Let Y1, Y2, . . . , Yn be a random sample from a population with de...
 9.93E: Let Y1, Y2, . . . , Yn be a random sample from a population with de...
 9.94E: Suppose that is the MLE for a parameter ?. Let t (?) be a function ...
 9.95E: A random sample of n items is selected from the large number of ite...
 9.96E: Consider a random sample of size n from a normal population with me...
 9.97E: The geometric probability mass function is given by A random sample...
 9.98E: Refer to Exercise 9.97. What is the approximate variance of the MLE...
 9.99E: Consider the distribution discussed in Example 9.18. Use the method...
 9.100E: Suppose that Y1, Y2, . . . , Yn constitute a random sample of size ...
 9.101E: Let Y1, Y2, . . . , Yn denote a random sample of size n from a Pois...
 9.102E: Refer to Exercises 9.97 and 9.98. If a sample of size 30 yields = 4...
 9.103SE: A random sample of size n is taken from a population with a Rayleig...
 9.104SE: Suppose that Y1, Y2, . . . , Yn constitute a random sample from the...
 9.105SE: Refer to Exercise 9.38(b). Under the conditions outlined there, fin...
 9.106SE: Suppose that Y1, Y2, . . . , Yn denote a random sample from a Poiss...
 9.107SE: Suppose that a random sample of lengthoflife measurements, Y1, Y2...
 9.108SE: The MLE obtained in Exercise 9.107 is a function of the minimal suf...
 9.109SE: Suppose that n integers are drawn at random and with replacement fr...
 9.110SE: Refer to Exercise 9.109.a Find the MLE of N.b Show that E( ) is app...
 9.111SE: Refer to Exercise 9.110. Suppose that enemy tanks have serial numbe...
 9.112SE: Let Y1, Y2, . . . , Yn denote a random sample from a Poisson distri...
Solutions for Chapter 9: Mathematical Statistics with Applications 7th Edition
Full solutions for Mathematical Statistics with Applications  7th Edition
ISBN: 9780495110811
Solutions for Chapter 9
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their solutions. Since 112 problems in chapter 9 have been answered, more than 262939 students have viewed full stepbystep solutions from this chapter. This textbook survival guide was created for the textbook: Mathematical Statistics with Applications , edition: 7. Chapter 9 includes 112 full stepbystep solutions. Mathematical Statistics with Applications was written by and is associated to the ISBN: 9780495110811.

2 k p  factorial experiment
A fractional factorial experiment with k factors tested in a 2 ? p fraction with all factors tested at only two levels (settings) each

aerror (or arisk)
In hypothesis testing, an error incurred by failing to reject a null hypothesis when it is actually false (also called a type II 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

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

Axioms of probability
A set of rules that probabilities deined on a sample space must follow. See Probability

Backward elimination
A method of variable selection in regression that begins with all of the candidate regressor variables in the model and eliminates the insigniicant regressors one at a time until only signiicant regressors remain

Binomial random variable
A discrete random variable that equals the number of successes in a ixed number of Bernoulli trials.

Causal variable
When y fx = ( ) and y is considered to be caused by x, x is sometimes called a causal variable

Completely randomized design (or experiment)
A type of experimental design in which the treatments or design factors are assigned to the experimental units in a random manner. In designed experiments, a completely randomized design results from running all of the treatment combinations in random order.

Continuous distribution
A probability distribution for a continuous random variable.

Convolution
A method to derive the probability density function of the sum of two independent random variables from an integral (or sum) of probability density (or mass) functions.

Critical value(s)
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.

Crossed factors
Another name for factors that are arranged in a factorial experiment.

Defect
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.

Dependent variable
The response variable in regression or a designed experiment.

Distribution function
Another name for a cumulative distribution function.

F distribution.
The distribution of the random variable deined as the ratio of two independent chisquare random variables, each divided by its number of degrees of freedom.

Ftest
Any test of signiicance involving the F distribution. The most common Ftests are (1) testing hypotheses about the variances or standard deviations of two independent normal distributions, (2) testing hypotheses about treatment means or variance components in the analysis of variance, and (3) testing signiicance of regression or tests on subsets of parameters in a regression model.

Generator
Effects in a fractional factorial experiment that are used to construct the experimental tests used in the experiment. The generators also deine the aliases.

Geometric mean.
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 .