 4.4.59: Let X 5 the time between two successive arrivals at thedriveup win...
 4.4.60: Let X denote the distance (m) that an animal moves fromits birth si...
 4.4.61: Data collected at Toronto Pearson International Airportsuggests tha...
 4.4.62: The article Microwave Observations of DailyAntarctic SeaIce Edge Ex...
 4.4.63: A consumer is trying to decide between two longdistancecalling pla...
 4.4.64: Evaluate the following:a. G(6) b. G(5/2)c. F(4; 5) (the incomplete ...
 4.4.65: Let X denote the data transfer time (ms) in a grid computingsystem ...
 4.4.66: The twoparameter gamma distribution can be generalizedby introduci...
 4.4.67: Suppose that when a transistor of a certain type is subjectedto an ...
 4.4.68: The special case of the gamma distribution in which a isa positive ...
 4.4.69: A system consists of five identical components connectedin series a...
 4.4.70: If X has an exponential distribution with parameter l,derive a gene...
 4.4.71: a. The event {X2 # y} is equivalent to what event involvingX itself...
Solutions for Chapter 4.4: The Exponential and Gamma Distributions
Full solutions for Probability and Statistics for Engineering and the Sciences  9th Edition
ISBN: 9781305251809
Solutions for Chapter 4.4: The Exponential and Gamma Distributions
Get Full SolutionsChapter 4.4: The Exponential and Gamma Distributions includes 13 full stepbystep solutions. This expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Probability and Statistics for Engineering and the Sciences, edition: 9. Since 13 problems in chapter 4.4: The Exponential and Gamma Distributions have been answered, more than 89140 students have viewed full stepbystep solutions from this chapter. Probability and Statistics for Engineering and the Sciences was written by and is associated to the ISBN: 9781305251809.

Additivity property of x 2
If two independent random variables X1 and X2 are distributed as chisquare with v1 and v2 degrees of freedom, respectively, Y = + X X 1 2 is a chisquare random variable with u = + v v 1 2 degrees of freedom. This generalizes to any number of independent chisquare random variables.

Alternative hypothesis
In statistical hypothesis testing, this is a hypothesis other than the one that is being tested. The alternative hypothesis contains feasible conditions, whereas the null hypothesis speciies conditions that are under test

Biased estimator
Unbiased estimator.

Causal variable
When y fx = ( ) and y is considered to be caused by x, x is sometimes called a causal variable

Chisquare (or chisquared) random variable
A continuous random variable that results from the sum of squares of independent standard normal random variables. It is a special case of a gamma random variable.

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.

Conditional probability distribution
The distribution of a random variable given that the random experiment produces an outcome in an event. The given event might specify values for one or more other random variables

Continuity correction.
A correction factor used to improve the approximation to binomial probabilities from a normal distribution.

Correlation matrix
A square matrix that contains the correlations among a set of random variables, say, XX X 1 2 k , ,…, . The main diagonal elements of the matrix are unity and the offdiagonal elements rij are the correlations between Xi and Xj .

Cumulative distribution function
For a random variable X, the function of X deined as PX x ( ) ? that is used to specify the probability distribution.

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

Defect
Used in statistical quality control, a defect is a particular type of nonconformance to speciications or requirements. Sometimes defects are classiied into types, such as appearance defects and functional defects.

Discrete uniform random variable
A discrete random variable with a inite range and constant probability mass function.

Distribution function
Another name for a cumulative distribution function.

Error propagation
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.

Estimate (or point estimate)
The numerical value of a point estimator.

Firstorder model
A model that contains only irstorder terms. For example, the irstorder response surface model in two variables is y xx = + ?? ? ? 0 11 2 2 + + . A irstorder model is also called a main effects model

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

Geometric random variable
A discrete random variable that is the number of Bernoulli trials until a success occurs.

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 .