- 4.2.11: Let X denote the amount of time a book on two-hourreserve is actual...
- 4.2.12: The cdf for X (5 measurement error) of Exercise 3 isF(x) 550 x , 22...
- 4.2.13: Example 4.5 introduced the concept of time headway intraffic flow a...
- 4.2.14: The article Modeling Sediment and Water ColumnInteractions for Hydr...
- 4.2.15: Let X denote the amount of space occupied by an articleplaced in a ...
- 4.2.16: The article A Model of Pedestrians Waiting Timesfor Street Crossing...
- 4.2.17: Let X have a uniform distribution on the interval [A, B].a. Obtain ...
- 4.2.18: Let X denote the voltage at the output of a microphone,and suppose ...
- 4.2.19: Let X be a continuous rv with cdfF(x) 55 0 x # 0x4 31 1 ln14x24 0 ,...
- 4.2.20: Consider the pdf for total waiting time Y for two busesf( y) 55125 ...
- 4.2.21: An ecologist wishes to mark off a circular samplingregion having ra...
- 4.2.22: The weekly demand for propane gas (in 1000s of gallons)from a parti...
- 4.2.23: If the temperature at which a certain compound melts isa random var...
- 4.2.24: Let X have the Pareto pdff(x; k, u) 5 Hk ? ukxk11 x $ u0 x , uintro...
- 4.2.25: Let X be the temperature in 8C at which a certain chemicalreaction ...
- 4.2.26: Let X be the total medical expenses (in 1000s of dollars)incurred b...
- 4.2.27: When a dart is thrown at a circular target, consider the locationof...
Solutions for Chapter 4.2: Cumulative Distribution Functions and Expected Values
Full solutions for Probability and Statistics for Engineering and the Sciences | 9th Edition
Adjusted R 2
A variation of the R 2 statistic that compensates for the number of parameters in a regression model. Essentially, the adjustment is a penalty for increasing the number of parameters in the model. Alias. In a fractional factorial experiment when certain factor effects cannot be estimated uniquely, they are said to be aliased.
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
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
Axioms of probability
A set of rules that probabilities deined on a sample space must follow. See Probability
An equation for a conditional probability such as PA B ( | ) in terms of the reverse conditional probability PB A ( | ).
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.
The variance of the conditional probability distribution of a random variable.
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.
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 dimensionless measure of the linear association between two variables, usually lying in the interval from ?1 to +1, with zero indicating the absence of correlation (but not necessarily the independence of the two variables).
Cumulative distribution function
For a random variable X, the function of X deined as PX x ( ) ? that is used to specify the probability distribution.
Degrees of freedom.
The number of independent comparisons that can be made among the elements of a sample. The term is analogous to the number of degrees of freedom for an object in a dynamic system, which is the number of independent coordinates required to determine the motion of the object.
Deming’s 14 points.
A management philosophy promoted by W. Edwards Deming that emphasizes the importance of change and quality
Discrete uniform random variable
A discrete random variable with a inite range and constant probability mass function.
A study in which a sample from a population is used to make inference to the population. See Analytic study
Error of estimation
The difference between an estimated value and the true value.
A subset of a sample space.
A property of a collection of events that indicates that their union equals the sample space.
In statistical quality control, that portion of a number of units or the output of a process that is defective.
Effects in a fractional factorial experiment that are used to construct the experimental tests used in the experiment. The generators also deine the aliases.