- 4.3.1E: Let X and Y have the joint pmf (a) Display the joint pmf and the ma...
- 4.3.2E: Let the joint pmf f (x, y) of X and Y be given by the following: Fi...
- 4.3.3E: Let W equal the weight of laundry soap in a 1-kilogram box that is ...
- 4.3.5E: Let X and Y have a trinomial distribution with n = 2, pX = 1/4, and...
- 4.3.6E: An insurance company sells both homeowners’ insurance and automobil...
- 4.3.7E: Using the joint pmf from Exercise 4.2-3, find the value of E(Y | x)...
- 4.3.9E: Let X and Y have a uniform distribution on the set of points with i...
- 4.3.10E: Let and find:
- 126.96.36.199-1: Let X and Y have the joint pmf f(x, y) = x + y 32 , x = 1, 2, y = 1...
- 188.8.131.52-2: Let the joint pmf f(x, y) of X and Y be given by the following: (x,...
- 184.108.40.206-3: Let W equal the weight of laundry soap in a 1-kilogram box that is ...
- 220.127.116.11-4: The alleles for eye color in a certain male fruit fly are (R, W). T...
- 18.104.22.168-5: Let X and Y have a trinomial distribution with n = 2, pX = 1/4, and...
- 22.214.171.124-6: An insurance company sells both homeowners insurance and automobile...
- 126.96.36.199-7: Using the joint pmf from Exercise 4.2-3, find the value of E(Y | x)...
- 188.8.131.52-8: A fair six-sided die is rolled 30 independent times. Let X be the n...
- 184.108.40.206-9: Let X and Y have a uniform distribution on the set of points with i...
- 220.127.116.11-10: Let fX (x) = 1/10, x = 0, 1, 2, ... , 9, and h(y | x) = 1/(10 x), y...
- 18.104.22.168-11: Choose a random integer X from the interval [0, 4]. Then choose a r...
Solutions for Chapter 4.3: Bivariate Distributions
Full solutions for Probability and Statistical Inference | 9th 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
Axioms of probability
A set of rules that probabilities deined on a sample space must follow. See Probability
Binomial random variable
A discrete random variable that equals the number of successes in a ixed number of Bernoulli trials.
The portion of the variability in a set of observations that is due to only random forces and which cannot be traced to speciic sources, such as operators, materials, or equipment. Also called a common cause.
A subset selected without replacement from a set used to determine the number of outcomes in events and sample spaces.
An experiment in which the treatments (experimental conditions) that are to be studied are included in the experiment. The data from the experiment are used to evaluate the treatments.
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.
See Control chart.
In regression, Cook’s distance is a measure of the inluence of each individual observation on the estimates of the regression model parameters. It expresses the distance that the vector of model parameter estimates with the ith observation removed lies from the vector of model parameter estimates based on all observations. Large values of Cook’s distance indicate that the observation is inluential.
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 distribution function
For a random variable X, the function of X deined as PX x ( ) ? that is used to specify the probability distribution.
Deming’s 14 points.
A management philosophy promoted by W. Edwards Deming that emphasizes the importance of change and quality
Another name for a probability density function
An experiment in which the tests are planned in advance and the plans usually incorporate statistical models. See Experiment
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.
An analysis of how the variance of the random variable that represents that output of a system depends on the variances of the inputs. A formula exists when the output is a linear function of the inputs and the formula is simpliied if the inputs are assumed to be independent.
Exponential random variable
A series of tests in which changes are made to the system under study
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