- 6.8.1E: Let Y be the sum of the observations of a random sample from a Pois...
- 6.8.2E: Let X1,X2, . . . ,Xn be a random sample from a gamma distribution w...
- 6.8.3E: In Example 6.8-2, take n = 30, ? = 15, and ? = 5.(a) Using the squa...
- 6.8.4E: Consider a random sample X1,X2, . . . ,Xn from a distribution with ...
- 6.8.5E: In Example 6.8-3, suppose the loss function |? ? w(Y)| is used.What...
- 6.8.6E: Let Y be the largest order statistic of a random sample of size n f...
- 6.8.7E: Refer to Example 6.8-3. Suppose we select ?20=d?2, where ?2 is know...
- 188.8.131.52-1: Let Y be the sum of the observations of a random sample from a Pois...
- 184.108.40.206-2: Let X1, X2, ... , Xn be a random sample from a gamma distribution w...
- 220.127.116.11-3: In Example 6.8-2, take n = 30, = 15, and = 5. (a) Using the squared...
- 18.104.22.168-4: Consider a random sample X1, X2, ... , Xn from a distribution with ...
- 22.214.171.124-5: In Example 6.8-3, suppose the loss function | w(Y)| is used. What i...
- 126.96.36.199-6: Let Y be the largest order statistic of a random sample of size n f...
- 188.8.131.52-7: Refer to Example 6.8-3. Suppose we select 2 0 = d2, where 2 is know...
- 184.108.40.206-8: Consider the likelihood function L(, , 2) of Section 6.5. Let and b...
Solutions for Chapter 6.8: Point Estimation
Full solutions for Probability and Statistical Inference | 9th Edition
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.
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.
The mean of the conditional probability distribution of a random variable.
Conditional probability distribution
The distribution of a random variable given that the random experiment produces an outcome in an event. The given event might specify values for one or more other random variables
A correction factor used to improve the approximation to binomial probabilities from a normal distribution.
Continuous random variable.
A random variable with an interval (either inite or ininite) of real numbers for its range.
Continuous uniform random variable
A continuous random variable with range of a inite interval and a constant probability density function.
Formulas used to determine the number of elements in sample spaces and events.
Cumulative sum control chart (CUSUM)
A control chart in which the point plotted at time t is the sum of the measured deviations from target for all statistics up to time t
An experiment in which the tests are planned in advance and the plans usually incorporate statistical models. See Experiment
Discrete uniform random variable
A discrete random variable with a inite range and constant probability mass function.
Erlang random variable
A continuous random variable that is the sum of a ixed number of independent, exponential random variables.
Estimate (or point estimate)
The numerical value of a point estimator.
Estimator (or point estimator)
A procedure for producing an estimate of a parameter of interest. An estimator is usually a function of only sample data values, and when these data values are available, it results in an estimate of the parameter of interest.
A subset of a 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 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.
Gamma random variable
A random variable that generalizes an Erlang random variable to noninteger values of the parameter r
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 random variable
A discrete random variable that is the number of Bernoulli trials until a success occurs.