- 7.6.1: Suppose that X1,...,Xn form a random sample from a distribution wit...
- 7.6.2: Suppose that X1,...,Xn form a random sample from a Poisson distribu...
- 7.6.3: Suppose that X1,...,Xn form a random sample from an exponential dis...
- 7.6.4: Suppose that the lifetime of a certain type of lamp has an exponent...
- 7.6.5: Suppose that X1,...,Xn form a random sample from the uniform distri...
- 7.6.6: Suppose that X1,...,Xn form a random sample from a normal distribut...
- 7.6.7: For the conditions of Exercise 6, find the M.L.E. of = Pr(X > 2).
- 7.6.8: Suppose that X1,...,Xn form a random sample from a gamma distributi...
- 7.6.9: Suppose that X1,...,Xn form a random sample from a gamma distributi...
- 7.6.10: Suppose that X1,...,Xn form a random sample from a beta distributio...
- 7.6.11: Suppose that X1,...,Xn form a random sample of size n from the unif...
- 7.6.12: Suppose that X1,...,Xn form a random sample from an exponential dis...
- 7.6.13: Suppose that X1,...,Xn form a random sample from a distribution for...
- 7.6.14: Suppose that a scientist desires to estimate the proportion p of mo...
- 7.6.15: Suppose that 21 observations are taken at random from an exponentia...
- 7.6.16: Suppose that each of two statisticians A and B must estimate a cert...
- 7.6.17: Suppose that each of two statisticians A and B must estimate a cert...
- 7.6.18: Prove that the method of moments estimator for the parameter of a B...
- 7.6.19: Prove that the method of moments estimator for the parameter of an ...
- 7.6.20: Prove that the method of moments estimator of the mean of a Poisson...
- 7.6.21: Prove that the method of moments estimators of the mean and varianc...
- 7.6.22: Let X1,...,Xn be a random sample from the uniform distribution on t...
- 7.6.23: Suppose that X1,...,Xn form a random sample from the beta distribut...
- 7.6.24: Suppose that the two-dimensional vectors (X1, Y1), (X2, Y2), . . . ...
- 7.6.25: Consider again the situation described in Exercise 24. This time, s...
Solutions for Chapter 7.6: Estimation
Full solutions for Probability and Statistics | 4th Edition
Additivity property of x 2
If two independent random variables X1 and X2 are distributed as chi-square with v1 and v2 degrees of freedom, respectively, Y = + X X 1 2 is a chi-square random variable with u = + v v 1 2 degrees of freedom. This generalizes to any number of independent chi-square random variables.
See Arithmetic mean.
Axioms of probability
A set of rules that probabilities deined on a sample space must follow. See Probability
Sequences of independent trials with only two outcomes, generally called “success” and “failure,” in which the probability of success remains constant.
The joint probability distribution of two random variables.
Conditional probability density function
The probability density function of the conditional probability distribution of a continuous 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 linear function of treatment means with coeficients that total zero. A contrast is a summary of treatment means that is of interest in an experiment.
Another name for factors that are arranged in a factorial experiment.
An expression sometimes used for nonlinear regression models or polynomial regression models.
A concept in parameter estimation that uses the variances of different estimators; essentially, an estimator is more eficient than another estimator if it has smaller variance. When estimators are biased, the concept requires modiication.
A model to relate a response to one or more regressors or factors that is developed from data obtained from the system.
A property of a collection of events that indicates that their union equals the sample space.
Extra sum of squares method
A method used in regression analysis to conduct a hypothesis test for the additional contribution of one or more variables to a model.
Any test of signiicance involving the F distribution. The most common F-tests are (1) testing hypotheses about the variances or standard deviations of two independent normal distributions, (2) testing hypotheses about treatment means or variance components in the analysis of variance, and (3) testing signiicance of regression or tests on subsets of parameters in a regression model.
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
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.
In statistical quality control, that portion of a number of units or the output of a process that is defective.
Fraction defective control chart
See P chart
A function that is used to determine properties of the probability distribution of a random variable. See Moment-generating function