- 3.6.1: A batch of 1M RAM chips are purchased from two different semiconduc...
- 3.6.2: Let X and Y have joint pdff(x, y) =1 , x2 + y2 1,0, otherwise.Deter...
- 3.6.3: Consider a series connection of two components, with respective lif...
- 3.6.4: If the random variables B and C are independent and uniformly distr...
- 3.6.5: Let the joint pdf of X and Y be given byf(x, y) = 121 2 expx2 2xy +...
Solutions for Chapter 3.6: Jointly Distributed Random Variables
Full solutions for Probability and Statistics with Reliability, Queuing, and Computer Science Applications | 2nd Edition
The arithmetic mean of a set of numbers x1 , x2 ,…, xn is their sum divided by the number of observations, or ( / )1 1 n xi t n ? = . The arithmetic mean is usually denoted by x , and is often called the average
Data consisting of counts or observations that can be classiied into categories. The categories may be descriptive.
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.
If it is possible to write a probability statement of the form PL U ( ) ? ? ? ? = ?1 where L and U are functions of only the sample data and ? is a parameter, then the interval between L and U is called a conidence interval (or a 100 1( )% ? ? conidence interval). The interpretation is that a statement that the parameter ? lies in this interval will be true 100 1( )% ? ? of the times that such a statement is made
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.
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 the most general usage, a measure of the interdependence among data. The concept may include more than two variables. The term is most commonly used in a narrow sense to express the relationship between quantitative variables or ranks.
Defect concentration diagram
A quality tool that graphically shows the location of defects on a part or in a process.
W. Edwards Deming (1900–1993) was a leader in the use of statistical quality control.
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
Discrete random variable
A random variable with a inite (or countably ininite) range.
Discrete uniform random variable
A discrete random variable with a inite range and constant probability mass function.
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).
Another name for a cumulative distribution function.
A study in which a sample from a population is used to make inference to the population. See Analytic study
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.
The distribution of the random variable deined as the ratio of two independent chi-square random variables, each divided by its number of degrees of freedom.
Fisher’s least signiicant difference (LSD) method
A series of pair-wise hypothesis tests of treatment means in an experiment to determine which means differ.
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.