- 3.1.1: A concrete beam may fail either by shear (S) or flexure (F). Suppos...
- 3.1.2: Give three examples of Bernoulli rvs (other than thosein the text).
- 3.1.3: Using the experiment in Example 3.3, define two more random variabl...
- 3.1.4: Let X = the number of nonzero digits in a randomlyselected 4-digit ...
- 3.1.5: If the sample space S is an infinite set, does thisnecessar ily imp...
- 3.1.6: Starting at a fixed time, each car entering an intersectionis obser...
- 3.1.7: For each random variable defined here, describe the setof possible ...
- 3.1.8: Each time a component is tested, the trial is a success (S) orfailu...
- 3.1.9: An individual named Claudius is located at the point 0 inthe accomp...
- 3.1.10: The number of pumps in use at both a six-pump stationand a four-pum...
Solutions for Chapter 3.1: Random Variables
Full solutions for Probability and Statistics for Engineering and the Sciences | 9th Edition
Sequences of independent trials with only two outcomes, generally called “success” and “failure,” in which the probability of success remains constant.
When y fx = ( ) and y is considered to be caused by x, x is sometimes called a causal variable
A chart used to organize the various potential causes of a problem. Also called a ishbone diagram.
Conditional probability density function
The probability density function of the conditional probability distribution of a continuous random variable.
A graphical display used to monitor a process. It usually consists of a horizontal center line corresponding to the in-control value of the parameter that is being monitored and lower and upper control limits. The control limits are determined by statistical criteria and are not arbitrary, nor are they related to speciication limits. If sample points fall within the control limits, the process is said to be in-control, or free from assignable causes. Points beyond the control limits indicate an out-of-control process; that is, assignable causes are likely present. This signals the need to ind and remove the assignable causes.
The value of a statistic corresponding to a stated signiicance level as determined from the sampling distribution. For example, if PZ z PZ ( )( .) . ? =? = 0 025 . 1 96 0 025, then z0 025 . = 1 9. 6 is the critical value of z at the 0.025 level of signiicance. Crossed factors. Another name for factors that are arranged in a factorial experiment.
Cumulative sum control chart (CUSUM)
A control chart in which the point plotted at time t is the sum of the measured deviations from target for all statistics up to time t
An expression sometimes used for nonlinear regression models or polynomial regression models.
Defects-per-unit control chart
See U chart
W. Edwards Deming (1900–1993) was a leader in the use of statistical quality control.
A matrix that provides the tests that are to be conducted in an experiment.
The amount of variability exhibited by data
Error mean square
The error sum of squares divided by its number of degrees of freedom.
A subset of a sample space.
A series of tests in which changes are made to the system under study
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.
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.
Gamma random variable
A random variable that generalizes an Erlang random variable to noninteger values of the parameter r
Goodness of fit
In general, the agreement of a set of observed values and a set of theoretical values that depend on some hypothesis. The term is often used in itting a theoretical distribution to a set of observations.
In multiple regression, the matrix H XXX X = ( ) ? ? -1 . This a projection matrix that maps the vector of observed response values into a vector of itted values by yˆ = = X X X X y Hy ( ) ? ? ?1 .