- 4.2.1: Two fair dice are rolled and the absolute value of the difference o...
- 4.2.2: From an urn that contains five red, five white, and five blue chips...
- 4.2.3: In a society of population N, the probability is p that a person ha...
- 4.2.4: The side measurement of a plastic die, manufactured by factory A, i...
- 4.2.5: F, the distribution function of a random variable X, is given by F ...
- 4.2.6: From families with three children a family is chosen at random. Let...
- 4.2.7: A grocery store sells X hundred kilograms of rice every day, where ...
- 4.2.8: Let X be a random variable with distribution function F. For p (0 <...
- 4.2.9: A random variable X is called symmetric about 0 if for all x R , P ...
- 4.2.10: Determine if the following is a distribution function. F (t) = 1 1 ...
- 4.2.11: Determine if the following is a distribution function. F (t) = t 1 ...
- 4.2.12: Determine if the following is a distribution function. F (t) = B (1...
- 4.2.13: Airline A has commuter flights every 45 minutes from San Francisco ...
- 4.2.14: A scientific calculator can generate two-digit random numbers. That...
- 4.2.15: In a small town there are 40 taxis, numbered 1 to 40. Three taxis a...
- 4.2.16: Let X be a randomly selected point from the interval(0, 3). What is...
- 4.2.17: Let X be a random point selected from the interval (0, 1). Calculat...
- 4.2.18: In the United States, the number of twin births is approximately 1 ...
- 4.2.19: Let the time until a new car breaks down be denoted by X, and let Y...
Solutions for Chapter 4.2: Distribution Functions and Discrete Random Variables
Full solutions for Fundamentals of Probability, with Stochastic Processes | 3rd Edition
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
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.
Axioms of probability
A set of rules that probabilities deined on a sample space must follow. See Probability
The joint probability distribution of two random variables.
Bivariate normal distribution
The joint distribution of two normal random variables
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.
A subset selected without replacement from a set used to determine the number of outcomes in events and sample spaces.
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.
Components of variance
The individual components of the total variance that are attributable to speciic sources. This usually refers to the individual variance components arising from a random or mixed model analysis of variance.
The mean of the conditional probability distribution of a random variable.
A method to derive the probability density function of the sum of two independent random variables from an integral (or sum) of probability density (or mass) functions.
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 .
Another name for factors that are arranged in a factorial experiment.
An expression sometimes used for nonlinear regression models or polynomial regression models.
The response variable in regression or a designed experiment.
A probability distribution for a discrete random variable
Estimate (or point estimate)
The numerical value of a point estimator.
Any test of signiicance involving the F distribution. The most common F-tests are (1) testing hypotheses about the variances or standard deviations of two independent normal distributions, (2) testing hypotheses about treatment means or variance components in the analysis of variance, and (3) testing signiicance of regression or tests on subsets of parameters in a regression model.
Fixed factor (or fixed effect).
In analysis of variance, a factor or effect is considered ixed if all the levels of interest for that factor are included in the experiment. Conclusions are then valid about this set of levels only, although when the factor is quantitative, it is customary to it a model to the data for interpolating between these levels.
In statistical quality control, that portion of a number of units or the output of a process that is defective.