 4.4.1.1: Suppose that X U(3,8). Find: (a) E(X) (b) The standard deviation of...
 4.4.1.2: A new battery supposedly with a charge of 1.5 volts actually has a ...
 4.4.1.3: A computer randomnumber generator produces numbers that have a uni...
 4.4.1.4: The lengths in meters of pieces of scrap wood found on a building s...
 4.4.1.5: Suppose that a metal pin has a diameter that has a uniform distribu...
 4.4.1.6: When employees undergo an evaluation, their scores are independenta...
 4.4.2.1: Use integration by parts to show that if X has an exponential distr...
 4.4.2.2: Suppose that you are waiting for a friend to call you and that the ...
 4.4.2.3: The time in days between breakdowns of a machine is exponentially d...
 4.4.2.4: A researcher plants 12 seeds whose germination times in days are in...
 4.4.2.5: A double exponential distribution, often called a Laplace distribut...
 4.4.2.6: Imperfections in an optical ber are distributed according to a Pois...
 4.4.2.7: The arrival times of workers at a factory rstaid room satisfy a Po...
 4.4.2.8: Engineers observe that about 90% of graphite samples fracture withi...
 4.4.2.9: Consider a Poisson process with parameter =0.8. (a) What is the pro...
 4.4.2.10: The lengths of telephone calls can be modeled by an exponential dis...
 4.4.2.11: Customers arrive at a service window according to a Poisson process...
 4.4.2.12: Suppose that components have failure times that are independent and...
 4.4.2.13: As a metal detector is passed over the ground, signals are received...
 4.4.2.14: Ninety identical electrical circuits are monitored at an extreme te...
 4.4.3.1: Use integration by parts to show that (k) = (k1) ( k1) for k > 1. U...
 4.4.3.2: Recall that if X1,...,Xk are independent random variables each havi...
 4.4.3.3: Use a computer package to nd both the probability density function ...
 4.4.3.4: A days sales in $1000 units at a gas station have a gamma distribut...
 4.4.3.5: Recall 4.2.6 concerning imperfections in an optical ber. Suppose th...
 4.4.3.6: Recall 4.2.7 concerning the arrivals at a factory rstaid room. (a)...
 4.4.3.7: Suppose that the time in minutes taken by a worker on an assembly l...
 4.4.4.1: Use the denition of the gamma function to derive the expectation an...
 4.4.4.2: Suppose that the random variable X has a Weibull distribution with ...
 4.4.4.3: Suppose that the random variable X has a Weibull distribution with ...
 4.4.4.4: The time to failure in hours of an electrical circuit subjected to ...
 4.4.4.5: A biologist models the time in minutes between the formation of a c...
 4.4.4.6: The lifetime in minutes of a mechanical component has a Weibulldist...
 4.4.4.7: Suppose that the time in days taken for bacteria cultures to develo...
 4.4.4.8: A physician conducts a study to investigate the time taken to recov...
 4.4.5.1: Consider the probability density function f (x) = Ax3 (1x)2 for 0 x...
 4.4.5.2: Consider the beta probability density function f (x) = Ax9 (1x)3 fo...
 4.4.5.3: Use a computer package to nd the probability density function and c...
 4.4.5.4: Suppose that the random variable X has a beta distribution with par...
 4.4.5.5: The purity of a chemical batch, expressed as a percentage, is equal...
 4.4.5.6: The proportion of tin in a metal alloy has a beta distribution with...
 4.4.8.1: A dial is spun and an angle is measured, which can be taken to be u...
 4.4.8.2: A commercial bleach eventually becomes ineffective because the chlo...
 4.4.8.3: A ship navigating through the southern regions of the North Atlanti...
 4.4.8.4: Calls arriving at a switchboard follow a Poisson process with param...
 4.4.8.5: Figure 4.25 shows the probability density function of a triangle di...
 4.4.8.6: The fermentation time in weeks required by a brewery for a particul...
 4.4.8.7: The proportion of a day that a tiger spends hunting for food has a ...
 4.4.8.8: The starting time of a class is uniformly distributed between 10:00...
 4.4.8.9: Anherbalistndsthatabout25%ofplantssproutwithin35 days, and that abo...
 4.4.8.10: The strength of a chemical solution is measured on a scale between ...
 4.4.8.11: Suppose that visits to a website can be modeled by a Poisson proces...
 4.4.8.12: A hole is drilled into the Antarctic ice shelf and a core is extrac...
 4.4.8.13: Are the following statements true or false? (a) If a Beta distribut...
 4.4.8.14: Are the following statements true or false? (a) If a Beta distribut...
 4.4.8.15: Consider a Poisson process with parameter =8. (a) Consider an inter...
 4.4.8.16: Suppose that customer waiting times are independent and can be mode...
Solutions for Chapter 4: Continuous Probability Distributions
Full solutions for Probability and Statistics for Engineers and Scientists  4th Edition
ISBN: 9781111827045
Solutions for Chapter 4: Continuous Probability Distributions
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their solutions. Probability and Statistics for Engineers and Scientists was written by and is associated to the ISBN: 9781111827045. This textbook survival guide was created for the textbook: Probability and Statistics for Engineers and Scientists, edition: 4. Since 57 problems in chapter 4: Continuous Probability Distributions have been answered, more than 11778 students have viewed full stepbystep solutions from this chapter. Chapter 4: Continuous Probability Distributions includes 57 full stepbystep solutions.

2 k factorial experiment.
A full factorial experiment with k factors and all factors tested at only two levels (settings) each.

2 k p  factorial experiment
A fractional factorial experiment with k factors tested in a 2 ? p fraction with all factors tested at only two levels (settings) each

aerror (or arisk)
In hypothesis testing, an error incurred by failing to reject a null hypothesis when it is actually false (also called a type II error).

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

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

Average
See Arithmetic mean.

Average run length, or ARL
The average number of samples taken in a process monitoring or inspection scheme until the scheme signals that the process is operating at a level different from the level in which it began.

Bayes’ estimator
An estimator for a parameter obtained from a Bayesian method that uses a prior distribution for the parameter along with the conditional distribution of the data given the parameter to obtain the posterior distribution of the parameter. The estimator is obtained from the posterior distribution.

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.

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.

Convolution
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.

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 .

Defectsperunit control chart
See U chart

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.

Ftest
Any test of signiicance involving the F distribution. The most common Ftests are (1) testing hypotheses about the variances or standard deviations of two independent normal distributions, (2) testing hypotheses about treatment means or variance components in the analysis of variance, and (3) testing signiicance of regression or tests on subsets of parameters in a regression model.

Fraction defective
In statistical quality control, that portion of a number of units or the output of a process that is defective.

Fraction defective control chart
See P chart

Gaussian distribution
Another name for the normal distribution, based on the strong connection of Karl F. Gauss to the normal distribution; often used in physics and electrical engineering applications

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 .

Hat matrix.
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 .