 6.6.1E: Let X1,X2, . . . ,Xn be a random sample from N(?, ?2), where ?2 is ...
 6.6.2E: Let X1,X2, . . . ,Xn denote a random sample from b(1, p). We know t...
 6.6.3E: (Continuation of Exercise 6.42.) In sampling from a normal distrib...
 6.6.4E: Find the Rao–Cramér lower bound, and thus the asymptotic variance o...
 6.6.6.61: Let X1, X2, ... , Xn be a random sample from N(, 2), where 2 is kno...
 6.6.6.62: Let X1, X2, ... , Xn denote a random sample from b(1, p). We know t...
 6.6.6.63: (Continuation of Exercise 6.42.) In sampling from a normal distrib...
 6.6.6.64: Find the RaoCramr lower bound, and thus the asymptotic variance of ...
Solutions for Chapter 6.6: Point Estimation
Full solutions for Probability and Statistical Inference  9th Edition
ISBN: 9780321923271
Solutions for Chapter 6.6: Point Estimation
Get Full SolutionsProbability and Statistical Inference was written by and is associated to the ISBN: 9780321923271. This expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Probability and Statistical Inference , edition: 9. Since 8 problems in chapter 6.6: Point Estimation have been answered, more than 108115 students have viewed full stepbystep solutions from this chapter. Chapter 6.6: Point Estimation includes 8 full stepbystep solutions.

Additivity property of x 2
If two independent random variables X1 and X2 are distributed as chisquare with v1 and v2 degrees of freedom, respectively, Y = + X X 1 2 is a chisquare random variable with u = + v v 1 2 degrees of freedom. This generalizes to any number of independent chisquare random variables.

Alternative hypothesis
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

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 limit theorem
The simplest form of the central limit theorem states that the sum of n independently distributed random variables will tend to be normally distributed as n becomes large. It is a necessary and suficient condition that none of the variances of the individual random variables are large in comparison to their sum. There are more general forms of the central theorem that allow ininite variances and correlated random variables, and there is a multivariate version of the theorem.

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.

Combination.
A subset selected without replacement from a set used to determine the number of outcomes in events and sample spaces.

Conditional mean
The mean of the conditional probability distribution of a random variable.

Conditional variance.
The variance of the conditional probability distribution of a random variable.

Continuous uniform random variable
A continuous random variable with range of a inite interval and a constant probability density function.

Covariance matrix
A square matrix that contains the variances and covariances among a set of random variables, say, X1 , X X 2 k , , … . The main diagonal elements of the matrix are the variances of the random variables and the offdiagonal elements are the covariances between Xi and Xj . Also called the variancecovariance matrix. When the random variables are standardized to have unit variances, the covariance matrix becomes the correlation matrix.

Defectsperunit control chart
See U chart

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

Experiment
A series of tests in which changes are made to the system under study

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

False alarm
A signal from a control chart when no assignable causes are present

Fisher’s least signiicant difference (LSD) method
A series of pairwise hypothesis tests of treatment means in an experiment to determine which means differ.

Forward selection
A method of variable selection in regression, where variables are inserted one at a time into the model until no other variables that contribute signiicantly to the model can be found.

Geometric random variable
A discrete random variable that is the number of Bernoulli trials until a success occurs.

Goodness of fit
In general, the agreement of a set of observed values and a set of theoretical values that depend on some hypothesis. The term is often used in itting a theoretical distribution to a set of observations.

Hat matrix.
In multiple regression, the matrix H XXX X = ( ) ? ? 1 . This a projection matrix that maps the vector of observed response values into a vector of itted values by yˆ = = X X X X y Hy ( ) ? ? ?1 .