- 8.3.1: Let the joint probability mass function of discrete random variable...
- 8.3.2: Let the joint probability density function of continuous random var...
- 8.3.3: An unbiased coin is flipped until the sixth head is obtained. If th...
- 8.3.4: Let the conditional probability density function of X given that Y ...
- 8.3.5: Let X and Y be independent discrete random variables. Prove that fo...
- 8.3.6: Let X and Y be continuous random variables with joint probability d...
- 8.3.7: Let X and Y be continuous random variables with joint probability d...
- 8.3.8: First a point Y is selected at random from the interval (0, 1). The...
- 8.3.9: Let (X, Y ) be a random point from a unit disk centered at the orig...
- 8.3.10: The joint probability density function of X and Y is given by f (x,...
- 8.3.11: Leon leaves his office every day at a random time between 4:30 P.M....
- 8.3.12: Show that if $ N (t): t 0 % is a Poisson process, the conditional d...
- 8.3.13: In a sequence of independent Bernoulli trials, let X be the number ...
- 8.3.14: A point is selected at random and uniformly from the region R = $ (...
- 8.3.15: Let $ N (t): t 0 % be a Poisson process. For s < t show that the co...
- 8.3.16: Cards are drawn from an ordinary deck of 52, one at a time, randoml...
- 8.3.17: A box contains 10 red and 12 blue chips. Suppose that 18 chips are ...
- 8.3.18: Let X and Y be continuous random variables with joint probability d...
- 8.3.19: A point (X, Y ) is selected randomly from the triangle with vertice...
- 8.3.20: Let X and Y be discrete random variables with joint probability mas...
- 8.3.21: The lifetimes of batteries manufactured by a certain company are id...
Solutions for Chapter 8.3: Conditional Distributions
Full solutions for Fundamentals of Probability, with Stochastic Processes | 3rd Edition
2 k p - factorial experiment
A fractional factorial experiment with k factors tested in a 2 ? p fraction with all factors tested at only two levels (settings) each
`-error (or `-risk)
In hypothesis testing, an error incurred by rejecting a null hypothesis when it is actually true (also called a type I error).
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
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
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
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.
Completely randomized design (or experiment)
A type of experimental design in which the treatments or design factors are assigned to the experimental units in a random manner. In designed experiments, a completely randomized design results from running all of the treatment combinations in random order.
A correction factor used to improve the approximation to binomial probabilities from a normal distribution.
Used in statistical quality control, a defect is a particular type of nonconformance to speciications or requirements. Sometimes defects are classiied into types, such as appearance defects and functional defects.
The response variable in regression or a designed experiment.
A probability distribution for a discrete random variable
Discrete random variable
A random variable with a inite (or countably ininite) range.
A model to relate a response to one or more regressors or factors that is developed from data obtained from the system.
Erlang random variable
A continuous random variable that is the sum of a ixed number of independent, exponential random variables.
Error of estimation
The difference between an estimated value and the true value.
The variance of an error term or component in a model.
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.
A signal from a control chart when no assignable causes are present
A method of variable selection in regression, where variables are inserted one at a time into the model until no other variables that contribute signiicantly to the model can be found.