 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 126641 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.

Analytic study
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

Average
See Arithmetic mean.

Bias
An effect that systematically distorts a statistical result or estimate, preventing it from representing the true quantity of interest.

Biased estimator
Unbiased estimator.

Categorical data
Data consisting of counts or observations that can be classiied into categories. The categories may be descriptive.

Central tendency
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.

Chance cause
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.

Chisquare (or chisquared) 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.

Control limits
See Control chart.

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.

Correlation matrix
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 offdiagonal elements rij are the correlations between Xi and Xj .

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.

Distribution function
Another name for a cumulative distribution function.

Erlang random variable
A continuous random variable that is the sum of a ixed number of independent, exponential random variables.

Exhaustive
A property of a collection of events that indicates that their union equals the sample space.

Exponential random variable
A series of tests in which changes are made to the system under study

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.

Fractional factorial experiment
A type of factorial experiment in which not all possible treatment combinations are run. This is usually done to reduce the size of an experiment with several factors.

Gamma random variable
A random variable that generalizes an Erlang random variable to noninteger values of the parameter r

Gaussian distribution
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