 7.9.1: . Suppose that the random variables X1,...,Xn form a random sample ...
 7.9.2: Suppose that the random variables X1,...,Xn form a random sample of...
 7.9.3: Consider again the conditions of Exercise 2, and let the estimator ...
 7.9.4: Consider again the conditions of Exercise 2. Let Yn = max{X1,...,Xn...
 7.9.5: Consider again the conditions of Exercises 2 and 4. Show that there...
 7.9.6: Suppose that X1,...,Xn form a random sample of size n (n 2) from th...
 7.9.7: Suppose that X1,...,Xn form a random sample from an exponential dis...
 7.9.8: uppose that a random sample of n observations is taken from a Poiss...
 7.9.9: . For every random variable X, show that E(X) E(X).
 7.9.10: Let X1,...,Xn form a random sample from a distribution for which th...
 7.9.11: Suppose that the variables X1,...,Xn form a random sample from a di...
 7.9.12: Suppose that X1,...,Xn form a sequence of n Bernoulli trials for wh...
 7.9.13: Suppose that X1,...,Xn form a random sample from a Poisson distribu...
 7.9.14: Consider again the conditions of Exercise 8. Determine the form of ...
 7.9.15: Find the M.L.E. of exp( + 0.125) in Example 7.9.5. Both the M.L.E. ...
 7.9.16: In Example 7.9.1, find the formula for p in terms of , the mean of ...
Solutions for Chapter 7.9: Estimation
Full solutions for Probability and Statistics  4th Edition
ISBN: 9780321500465
Solutions for Chapter 7.9: Estimation
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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).

Acceptance region
In hypothesis testing, a region in the sample space of the test statistic such that if the test statistic falls within it, the null hypothesis cannot be rejected. This terminology is used because rejection of H0 is always a strong conclusion and acceptance of H0 is generally a weak conclusion

Addition rule
A formula used to determine the probability of the union of two (or more) events from the probabilities of the events and their intersection(s).

Alias
In a fractional factorial experiment when certain factor effects cannot be estimated uniquely, they are said to be aliased.

Attribute control chart
Any control chart for a discrete random variable. See Variables control chart.

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

Bimodal distribution.
A distribution with two modes

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

Causeandeffect diagram
A chart used to organize the various potential causes of a problem. Also called a ishbone diagram.

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

Continuity correction.
A correction factor used to improve the approximation to binomial probabilities from a normal distribution.

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.

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.

Defectsperunit control chart
See U chart

Dispersion
The amount of variability exhibited by data

Enumerative study
A study in which a sample from a population is used to make inference to the population. See Analytic study

Error variance
The variance of an error term or component in a model.

Factorial experiment
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.

Finite population correction factor
A term in the formula for the variance of a hypergeometric random variable.

Generating function
A function that is used to determine properties of the probability distribution of a random variable. See Momentgenerating function