 59.s513: A random variable X has the discrete uniform distribution (a) Show ...
 59.s514: A random variable X has the Poisson distribution
 59.s515: The geometric random variable X has probability distribution f 1x2 ...
 59.s516: The chisquared random variable with k degrees of freedom has momen...
 59.s517: A continuous random variable X has the following probability distri...
 59.s518: The continuous uniform random variable X has density function (a) S...
 59.s519: A random variable X has the exponential distribution (a) Show that ...
 59.s520: A random variable X has the gamma distribution
 59.s521: Let X1, X2, . . . , Xr be independent exponential random variables ...
 59.s522: Suppose that Xi has a normal distribution with mean i and variance ...
 59.s523: Show that the moment generating function of the chisquared random ...
 59.s524: Continuation of Exercise S520. (a) Show that by expanding etX in a...
Solutions for Chapter 59: MOMENT GENERATING FUNCTIONS (CD ONLY)
Full solutions for Applied Statistics and Probability for Engineers  3rd Edition
ISBN: 9780471204541
Solutions for Chapter 59: MOMENT GENERATING FUNCTIONS (CD ONLY)
Get Full SolutionsThis textbook survival guide was created for the textbook: Applied Statistics and Probability for Engineers , edition: 3. Since 12 problems in chapter 59: MOMENT GENERATING FUNCTIONS (CD ONLY) have been answered, more than 19356 students have viewed full stepbystep solutions from this chapter. Applied Statistics and Probability for Engineers was written by and is associated to the ISBN: 9780471204541. This expansive textbook survival guide covers the following chapters and their solutions. Chapter 59: MOMENT GENERATING FUNCTIONS (CD ONLY) includes 12 full stepbystep solutions.

Alias
In a fractional factorial experiment when certain factor effects cannot be estimated uniquely, they are said to be aliased.

Arithmetic mean
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

Bivariate normal distribution
The joint distribution of two normal random variables

Center line
A horizontal line on a control chart at the value that estimates the mean of the statistic plotted on the chart. See Control chart.

Chance cause
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.

Confounding
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.

Continuous distribution
A probability distribution for a continuous random variable.

Control limits
See Control chart.

Correction factor
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 .

Crossed factors
Another name for factors that are arranged in a factorial experiment.

Defectsperunit control chart
See U chart

Designed experiment
An experiment in which the tests are planned in advance and the plans usually incorporate statistical models. See Experiment

Eficiency
A concept in parameter estimation that uses the variances of different estimators; essentially, an estimator is more eficient than another estimator if it has smaller variance. When estimators are biased, the concept requires modiication.

Erlang random variable
A continuous random variable that is the sum of a ixed number of independent, exponential random variables.

Exhaustive
A property of a collection of events that indicates that their union equals the sample space.

Exponential random variable
A series of tests in which changes are made to the system under study

Gamma random variable
A random variable that generalizes an Erlang random variable to noninteger values of the parameter r

Generating function
A function that is used to determine properties of the probability distribution of a random variable. See Momentgenerating function

Generator
Effects in a fractional factorial experiment that are used to construct the experimental tests used in the experiment. The generators also deine the aliases.

Harmonic mean
The harmonic mean of a set of data values is the reciprocal of the arithmetic mean of the reciprocals of the data values; that is, h n x i n i = ? ? ? ? ? = ? ? 1 1 1 1 g .