- 3.1: Two persons arrive at a train station, independently of each other,...
- 3.2: A polygraph operator detects innocent suspects as being guilty 3% o...
- 3.3: In statistical surveys where individuals are selected randomly and ...
- 3.4: Diseases D1, D2, and D3 cause symptom A with probabilities 0.5, 0.7...
- 3.5: Professor Stern has three cars. The probability that on a given day...
- 3.6: A bus traveling from Baltimore to New York breaks down at a random ...
- 3.7: Roads A, B, and C are the only escape routes from a state prison. P...
- 3.8: From an ordinary deck of 52 cards, 10 cards are drawn at random. If...
- 3.9: A fair die is thrown twice. If the second outcome is 6, what is the...
- 3.10: Suppose that 10 dice are thrown and we are told that among them at ...
- 3.11: Urns I and II contain three pennies and four dimes, and two pennies...
- 3.12: An experiment consists of first tossing an unbiased coin and then r...
- 3.13: Six fair dice are tossed independently. Find the probability that t...
- 3.14: Urn I contains 25 white and 20 black balls. Urn II contains 15 whit...
- 3.15: An urn contains nine red and one blue balls. A second urn contains ...
- 3.16: A fair coin is tossed. If the outcome is heads, a red hat is placed...
- 3.17: A child is lost at Epcot Center in Florida. The father of the child...
- 3.18: Solve the following problem, asked of Marilyn Vos Savant in the Ask...
- 3.19: A student at a certain university will pass the oral Ph.D. qualifyi...
- 3.20: Adam and three of his friends are playing bridge. (a) If, holding a...
Solutions for Chapter 3: Conditional Probability and Independence
Full solutions for Fundamentals of Probability, with Stochastic Processes | 3rd Edition
2 k factorial experiment.
A full factorial experiment with k factors and all factors tested at only two levels (settings) each.
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
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.
Attribute control chart
Any control chart for a discrete random variable. See Variables control chart.
Axioms of probability
A set of rules that probabilities deined on a sample space must follow. See Probability
A distribution with two modes
In experimental design, a group of experimental units or material that is relatively homogeneous. The purpose of dividing experimental units into blocks is to produce an experimental design wherein variability within blocks is smaller than variability between blocks. This allows the factors of interest to be compared in an environment that has less variability than in an unblocked experiment.
When y fx = ( ) and y is considered to be caused by x, x is sometimes called a causal variable
A chart used to organize the various potential causes of a problem. Also called a ishbone diagram.
Central composite design (CCD)
A second-order response surface design in k variables consisting of a two-level factorial, 2k axial runs, and one or more center points. The two-level factorial portion of a CCD can be a fractional factorial design when k is large. The CCD is the most widely used design for itting a second-order model.
Coeficient of determination
See R 2 .
A subset selected without replacement from a set used to determine the number of outcomes in events and sample spaces.
In hypothesis testing, this is the portion of the sample space of a test statistic that will lead to rejection of the null hypothesis.
Deming’s 14 points.
A management philosophy promoted by W. Edwards Deming that emphasizes the importance of change and quality
A study in which a sample from a population is used to make inference to the population. See Analytic study
Estimate (or point estimate)
The numerical value of a point estimator.
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.
Gamma random variable
A random variable that generalizes an Erlang random variable to noninteger values of the parameter r
A function that is used to determine properties of the probability distribution of a random variable. See Moment-generating function
Goodness of fit
In general, the agreement of a set of observed values and a set of theoretical values that depend on some hypothesis. The term is often used in itting a theoretical distribution to a set of observations.