- 4.3.1: Tossing a Die An experiment involves tossing asingle die. These are...
- 4.3.2: 2 A sample space S consists of five simple eventswith these probabi...
- 4.3.3: A sample space contains 10 simple events: E1,E2, . . . , E10. If P(...
- 4.3.4: Free Throws A particular basketball player hits70% of her free thro...
- 4.3.5: Four Coins A jar contains four coins: a nickel, adime, a quarter, a...
- 4.3.6: Preschool or Not? On the first day of kindergarten,the teacher rand...
- 4.3.7: The Urn bowl contains three redand two yellow balls. Two balls are ...
- 4.3.8: The Urn Problem, continued Refer to Exercise4.7. A ball is randomly...
- 4.3.9: Need Eyeglasses? A survey classified a largenumber of adults accord...
- 4.3.10: Roulette The game of roulette uses a wheelcontaining 38 pockets. Th...
- 4.3.11: Jury Duty Three people are randomly selectedto report for jury duty...
- 4.3.12: Jury Duty II Refer to Exercise 4.11. Supposethat there are six pros...
- 4.3.13: Tea Tasters A food company plans to conductan experiment to compare...
- 4.3.14: 100-Meter Run Four equally qualified runners,John, Bill, Ed, and Da...
- 4.3.15: Fruit Flies In a genetics experiment, theresearcher mated two Droso...
- 4.3.16: Creation Which of the following comes closestto your views on the o...
Solutions for Chapter 4.3: Calculating Probabilities Using Simple Events
Full solutions for Introduction to Probability and Statistics 1 | 14th 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.
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.
See Arithmetic mean.
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.
Sequences of independent trials with only two outcomes, generally called “success” and “failure,” in which the probability of success remains constant.
Binomial random variable
A discrete random variable that equals the number of successes in a ixed number of Bernoulli trials.
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.
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 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.
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).
Cumulative distribution function
For a random variable X, the function of X deined as PX x ( ) ? that is used to specify the probability distribution.
Defect concentration diagram
A quality tool that graphically shows the location of defects on a part or in a process.
An experiment in which the tests are planned in advance and the plans usually incorporate statistical models. See Experiment
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 property of a collection of events that indicates that their union equals the sample space.
The expected value of a random variable X is its long-term average or mean value. In the continuous case, the expected value of X is E X xf x dx ( ) = ?? ( ) ? ? where f ( ) x is the density function of the random variable X.
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.