- 4.8.1: Let > 0. A decision maker has a utility function for money of the f...
- 4.8.2: Consider three gambles X, Y, and Z for which the probability distri...
- 4.8.3: Determine which of the three gambles in Exercise 2 would be preferr...
- 4.8.4: Determine which of the three gambles in Exercise 2 would be preferr...
- 4.8.5: Consider a utility function U for which U (0) = 0 and U (100) = 1. ...
- 4.8.6: Consider a utility function U for which U (0) = 5, U (1) = 8, and U...
- 4.8.7: Suppose that a person must accept a gamble X of the following form:...
- 4.8.8: Determine the value of a that a person would choose in Exercise 7 i...
- 4.8.9: Determine the value of a that a person would choose in Exercise 7 i...
- 4.8.10: Consider four gambles X1, X2, X3, and X4, for which the probability...
- 4.8.11: Suppose that a person has a given fortune A > 0 and can bet any amo...
- 4.8.12: Determine the amount b that the person should bet in Exercise 11 if...
- 4.8.13: Determine the amount b that the person should bet in Exercise 11 if...
- 4.8.14: Determine the amount b that the person should bet in Exercise 11 if...
- 4.8.15: Suppose that a person has a lottery ticket from which she will win ...
- 4.8.16: Let Y be a random variable that we would like to predict. Suppose t...
- 4.8.17: Let Y be a random variable that we would like to predict. Suppose t...
Solutions for Chapter 4.8: Expectation
Full solutions for Probability and Statistics | 4th Edition
Analysis of variance (ANOVA)
A method of decomposing the total variability in a set of observations, as measured by the sum of the squares of these observations from their average, into component sums of squares that are associated with speciic deined sources of variation
A qualitative characteristic of an item or unit, usually arising in quality control. For example, classifying production units as defective or nondefective results in attributes data.
A method of variable selection in regression that begins with all of the candidate regressor variables in the model and eliminates the insigniicant regressors one at a time until only signiicant regressors remain
An estimator for a parameter obtained from a Bayesian method that uses a prior distribution for the parameter along with the conditional distribution of the data given the parameter to obtain the posterior distribution of the parameter. The estimator is obtained from the posterior distribution.
An attribute control chart that plots the total number of defects per unit in a subgroup. Similar to a defects-per-unit or U chart.
Chi-square (or chi-squared) random variable
A continuous random variable that results from the sum of squares of independent standard normal random variables. It is a special case of a gamma random variable.
Coeficient of determination
See R 2 .
The probability of an event given that the random experiment produces an outcome in another event.
A method to derive the probability density function of the sum of two independent random variables from an integral (or sum) of probability density (or mass) functions.
A dimensionless measure of the linear association between two variables, usually lying in the interval from ?1 to +1, with zero indicating the absence of correlation (but not necessarily the independence of the two variables).
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 .
Another name for factors that are arranged in a factorial experiment.
Cumulative distribution function
For a random variable X, the function of X deined as PX x ( ) ? that is used to specify the probability distribution.
The response variable in regression or a designed experiment.
An experiment in which the tests are planned in advance and the plans usually incorporate statistical models. See Experiment
The amount of variability exhibited by data
An analysis of how the variance of the random variable that represents that output of a system depends on the variances of the inputs. A formula exists when the output is a linear function of the inputs and the formula is simpliied if the inputs are assumed to be independent.
Finite population correction factor
A term in the formula for the variance of a hypergeometric random variable.
In statistical quality control, that portion of a number of units or the output of a process that is defective.
Another name for the normal distribution, based on the strong connection of Karl F. Gauss to the normal distribution; often used in physics and electrical engineering applications