- 9.9.1: Customers arrive at a bank at a Poisson rate .Suppose that two cust...
- 9.9.2: Cars cross a certain point in the highway in accordancewith a Poiss...
- 9.9.3: Suppose that in 9.2 Al is agile enough toescape from a single car, ...
- 9.9.4: Suppose that 3 white and 3 black balls are distributedin two urns i...
- 9.9.5: Consider Example 2a. If there is a 5050 chance ofrain today, comput...
- 9.9.6: Compute the limiting probabilities for the modelof 9.4.
- 9.9.7: A transition probability matrix is said to be doublystochastic ifMi...
- 9.9.8: On any given day, Buffy is either cheerful (c), so-so(s), or gloomy...
- 9.9.9: Suppose that whether it rains tomorrow dependson past weather condi...
- 9.9.10: A certain person goes for a run each morning.When he leaves his hou...
- 9.9.11: This problem refers to Example 2f.(a) Verify that the proposed valu...
Solutions for Chapter 9: First Course in Probability 8th Edition
Full solutions for First Course in Probability | 8th Edition
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
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.
All possible (subsets) regressions
A method of variable selection in regression that examines all possible subsets of the candidate regressor variables. Eficient computer algorithms have been developed for implementing all possible regressions
The arithmetic mean of a set of numbers x1 , x2 ,…, xn is their sum divided by the number of observations, or ( / )1 1 n xi t n ? = . The arithmetic mean is usually denoted by x , and is often called the average
The portion of the variability in a set of observations that can be traced to speciic causes, such as operators, materials, or equipment. Also called a special cause.
Asymptotic relative eficiency (ARE)
Used to compare hypothesis tests. The ARE of one test relative to another is the limiting ratio of the sample sizes necessary to obtain identical error probabilities for the two procedures.
Average run length, or ARL
The average number of samples taken in a process monitoring or inspection scheme until the scheme signals that the process is operating at a level different from the level in which it began.
Bivariate normal distribution
The joint distribution of two normal random variables
A probability distribution for a continuous random variable.
A square matrix that contains the correlations among a set of random variables, say, XX X 1 2 k , ,…, . The main diagonal elements of the matrix are unity and the off-diagonal elements rij are the correlations between Xi and Xj .
Formulas used to determine the number of elements in sample spaces and events.
Another name for factors that are arranged in a factorial experiment.
Defect concentration diagram
A quality tool that graphically shows the location of defects on a part or in a process.
Error sum of squares
In analysis of variance, this is the portion of total variability that is due to the random component in the data. It is usually based on replication of observations at certain treatment combinations in the experiment. It is sometimes called the residual sum of squares, although this is really a better term to use only when the sum of squares is based on the remnants of a model-itting process and not on replication.
A signal from a control chart when no assignable causes are present
Finite population correction factor
A term in the formula for the variance of a hypergeometric random variable.
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
In statistical quality control, that portion of a number of units or the output of a process that is defective.
Fractional factorial experiment
A type of factorial experiment in which not all possible treatment combinations are run. This is usually done to reduce the size of an experiment with several factors.
Effects in a fractional factorial experiment that are used to construct the experimental tests used in the experiment. The generators also deine the aliases.