- 8.7.1: Let X1,...,Xn be a random sample from the Poisson distribution with...
- 8.7.2: Suppose that X is a random variable whose distribution is completel...
- 8.7.3: For the conditions of Exercise 2, find an unbiased estimator of [E(...
- 8.7.4: Suppose that a random variable X has the geometric distribution wit...
- 8.7.5: Suppose that a random variable X has the Poisson distribution with ...
- 8.7.6: Suppose that X1,...,Xn form a random sample from the normal distrib...
- 8.7.7: . Suppose that X1,...,Xn form n Bernoulli trials for which the para...
- 8.7.8: Suppose that a random variable X has the geometric distribution wit...
- 8.7.9: . Suppose that a random variable X has the Poisson distribution wit...
- 8.7.10: Consider an infinite sequence of Bernoulli trials for which the par...
- 8.7.11: Suppose that a certain drug is to be administered to two different ...
- 8.7.12: Suppose that a certain population of individuals is composed of k d...
- 8.7.13: Suppose that X1,...,Xn form a random sample from a distribution for...
- 8.7.14: Suppose that X1,...,Xn form a random sample from the uniform distri...
- 8.7.15: Suppose that a random variable X can take only the five values x = ...
- 8.7.16: Reconsider the conditions of Exercise 3. Suppose that n = 2, and we...
Solutions for Chapter 8.7: Sampling Distributions of Estimators
Full solutions for Probability and Statistics | 4th Edition
Adjusted R 2
A variation of the R 2 statistic that compensates for the number of parameters in a regression model. Essentially, the adjustment is a penalty for increasing the number of parameters in the model. Alias. In a fractional factorial experiment when certain factor effects cannot be estimated uniquely, they are said to be aliased.
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
Sequences of independent trials with only two outcomes, generally called “success” and “failure,” in which the probability of success remains constant.
A distribution with two modes
When y fx = ( ) and y is considered to be caused by x, x is sometimes called a causal variable
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.
If it is possible to write a probability statement of the form PL U ( ) ? ? ? ? = ?1 where L and U are functions of only the sample data and ? is a parameter, then the interval between L and U is called a conidence interval (or a 100 1( )% ? ? conidence interval). The interpretation is that a statement that the parameter ? lies in this interval will be true 100 1( )% ? ? of the times that such a statement is made
A correction factor used to improve the approximation to binomial probabilities from a normal distribution.
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 .
Cumulative distribution function
For a random variable X, the function of X deined as PX x ( ) ? that is used to specify the probability distribution.
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.
An experiment in which the tests are planned in advance and the plans usually incorporate statistical models. See Experiment
Discrete random variable
A random variable with a inite (or countably ininite) range.
Estimate (or point estimate)
The numerical value of a point estimator.
A property of a collection of events that indicates that their union equals the sample space.
The distribution of the random variable deined as the ratio of two independent chi-square random variables, each divided by its number of degrees of freedom.
A model that contains only irstorder terms. For example, the irst-order response surface model in two variables is y xx = + ?? ? ? 0 11 2 2 + + . A irst-order model is also called a main effects model
An arrangement of the frequencies of observations in a sample or population according to the values that the observations take on
A function used in the probability density function of a gamma random variable that can be considered to extend factorials
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 .