- 3.3.1: If 5% of men and 0.25% of women are color blind, what is the probab...
- 3.3.2: Suppose that 40% of the students of a campus are women. If 20% of t...
- 3.3.3: Jim has three cars of different models: A, B, and C. The probabilit...
- 3.3.4: One of the cards of an ordinary deck of 52 cards is lost. What is t...
- 3.3.5: Two cards from an ordinary deck of 52 cards are missing. What is th...
- 3.3.6: Of the patients in a hospital, 20% of those with, and 35% of those ...
- 3.3.7: Suppose that 37% of a community are at least 45 years old. If 80% o...
- 3.3.8: A person has six guns. The probability of hitting a target when the...
- 3.3.9: A factory produces its entire output with three machines. Machines ...
- 3.3.10: Solve the following problem, from the Ask Marilyn column ofParade M...
- 3.3.11: Suppose that five coins, of which exactly three are gold, are distr...
- 3.3.12: In a town, 7/9th of the men and 3/5th of the women are married. In ...
- 3.3.13: A child gets lost in the Disneyland at the Epcot Center in Florida....
- 3.3.14: Suppose that there exist N families on the earth and that the maxim...
- 3.3.15: Let B be an event of a sample space S with P (B) > 0. For a subset ...
- 3.3.16: Suppose that 40% of the students on a campus, who are married to st...
- 3.3.17: Suppose that the probability that a new seed planted in a specific ...
- 3.3.18: Suppose that 10 good and three dead batteries are mixed up. Jack te...
- 3.3.19: A box contains 18 tennis balls, of which eight are new. Suppose tha...
- 3.3.20: From families with three children, a child is selected at random an...
- 3.3.21: Suppose that three numbers are selected one by one, at random and w...
- 3.3.22: Avril has certain standards for selecting her future husband. She h...
- 3.3.23: (Shrewd Prisoners Dilemma) Because of a prisoners constant supplica...
Solutions for Chapter 3.3: Law of Total Probability
Full solutions for Fundamentals of Probability, with Stochastic Processes | 3rd Edition
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
Binomial random variable
A discrete random variable that equals the number of successes in a ixed number of Bernoulli trials.
Data consisting of counts or observations that can be classiied into categories. The categories may be descriptive.
The tendency of data to cluster around some value. Central tendency is usually expressed by a measure of location such as the mean, median, or mode.
When a factorial experiment is run in blocks and the blocks are too small to contain a complete replicate of the experiment, one can run a fraction of the replicate in each block, but this results in losing information on some effects. These effects are linked with or confounded with the blocks. In general, when two factors are varied such that their individual effects cannot be determined separately, their effects are said to be confounded.
See Control chart.
A term used for the quantity ( / )( ) 1 1 2 n xi i n ? = that is subtracted from xi i n 2 ? =1 to give the corrected sum of squares deined as (/ ) ( ) 1 1 2 n xx i x i n ? = i ? . The correction factor can also be written as nx 2 .
In hypothesis testing, this is the portion of the sample space of a test statistic that will lead to rejection of the null hypothesis.
Cumulative normal distribution function
The cumulative distribution of the standard normal distribution, often denoted as ?( ) x and tabulated in Appendix Table II.
Defect concentration diagram
A quality tool that graphically shows the location of defects on a part or in a process.
The response variable in regression or a designed experiment.
Discrete random variable
A random variable with a inite (or countably ininite) range.
Distribution free method(s)
Any method of inference (hypothesis testing or conidence interval construction) that does not depend on the form of the underlying distribution of the observations. Sometimes called nonparametric method(s).
Error mean square
The error sum of squares divided by its number of degrees of freedom.
Estimate (or point estimate)
The numerical value of a point estimator.
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.
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.
A function used in the probability density function of a gamma random variable that can be considered to extend factorials
Geometric random variable
A discrete random variable that is the number of Bernoulli trials until a success occurs.