 4.4.1: Let X denote the amount of time for which a book on 2hour reserve ...
 4.4.10: Suppose the reaction temperature X (in C) in a certain chemical pro...
 4.4.11: The error involved in making a certain measurement is a continuous ...
 4.4.12: Let X denote the vibratory stress (psi) on a wind turbine blade at ...
 4.4.13: A college professor never finishes his lecture before the end of th...
 4.4.14: The actual tracking weight of a stereo cartridge that is set to tra...
 4.4.15: The time X (min) for a lab assistant to prepare the equipment for a...
 4.4.16: In commuting to work, I must first get on a bus near my house and t...
 4.4.17: Consider again the pdf of X time headway given in Example 4.5. What...
 4.4.18: A family of pdfs that has been used to approximate the distribution...
 4.4.19: The cdf of checkout duration X as described in Exercise 1 is x 0 F(...
 4.4.20: The cdf for X (measurement error) of Exercise 3 is 0 x 2 F(x) 1 2 3...
 4.4.21: Example 4.5 introduced the concept of time headway in traffic flow ...
 4.4.22: The article Modeling Sediment and Water Column Interactions for Hyd...
 4.4.23: Let X denote the amount of space occupied by an article placed in a...
 4.4.24: Answer parts (a)(f) of Exercise 15 with X lecture time past the hou...
 4.4.25: Let X have a uniform distribution on the interval [A, B]. a. Obtain...
 4.4.26: Let X denote the voltage at the output of a microphone, and suppose...
 4.4.27: Let X be a continuous rv with cdf 0 x 0 F(x) 4 x 1 ln 4 x 0 x 4 1 x...
 4.4.28: Consider the pdf for total waiting time Y for two buses 2 1 5 y 0 y...
 4.4.29: An ecologist wishes to mark off a circular sampling region having r...
 4.4.30: The weekly demand for propane gas (in 1000s of gallons) from a part...
 4.4.31: If the temperature at which a certain compound melts is a random va...
 4.4.32: Let X have the Pareto pdf f(x; k, ) k x k 1 k x 0 x introduced in E...
 4.4.33: Let X be the temperature in C at which a certain chemical reaction ...
 4.4.34: Let X be the total medical expenses (in 1000s of dollars) incurred ...
 4.4.35: When a dart is thrown at a circular target, consider the location o...
 4.4.36: Let Z be a standard normal random variable and calculate the follow...
 4.4.37: In each case, determine the value of the constant c that makes the ...
 4.4.38: Find the following percentiles for the standard normal distribution...
 4.4.39: Determine zfor the following: a. .0055 b. .09 c. .663
 4.4.40: If X is a normal rv with mean 80 and standard deviation 10, compute...
 4.4.41: Suppose the force acting on a column that helps to support a buildi...
 4.4.42: The article Reliability of DomesticWaste Biofilm Reactors (J. of E...
 4.4.43: Suppose the diameter at breast height (in.) of trees of a certain t...
 4.4.44: Spray drift is a constant concern for pesticide applicators and agr...
 4.4.45: Suppose that blood chloride concentration (mmol/L) has a normal dis...
 4.4.46: There are two machines available for cutting corks intended for use...
 4.4.47: a. If a normal distribution has 30 and 5, what is the 91st percenti...
 4.4.48: The article Monte Carlo SimulationTool for Better Understanding of ...
 4.4.49: The automatic opening device of a military cargo parachute has been...
 4.4.50: The temperature reading from a thermocouple placed in a constantte...
 4.4.51: The distribution of resistance for resistors of a certain type is k...
 4.4.52: If bolt thread length is normally distributed, what is the probabil...
 4.4.53: A machine that produces ball bearings has initially been set so tha...
 4.4.54: A machine that produces ball bearings has initially been set so tha...
 4.4.55: The weight distribution of parcels sent in a certain manner is norm...
 4.4.56: Suppose Appendix Table A.3 contained (z) only for z 0. Explain how ...
 4.4.57: Consider babies born in the normal range of 3743 weeks gestational ...
 4.4.58: In response to concerns about nutritional contents of fast foods, M...
 4.4.59: Chebyshevs inequality, (see Exercise 44 Chapter 3), is valid for co...
 4.4.60: . Let X denote the number of flaws along a 100m reel of magneticta...
 4.4.61: Let X have a binomial distribution with parameters n 25 and p. Calc...
 4.4.62: Suppose that 10% of all steel shafts produced by a certain process ...
 4.4.63: Suppose only 75% of all drivers in a certain state regularly wear a...
 4.4.64: Suppose only 75% of all drivers in a certain state regularly wear a...
 4.4.65: a. Show that if X has a normal distribution with parameters and , t...
 4.4.66: There is no nice formula for the standard normal cdf (z), but sever...
 4.4.67: Let X the time between two successive arrivals at the driveup wind...
 4.4.68: Let X denote the distance (m) that an animal moves from its birth s...
 4.4.69: Extensive experience with fans of a certain type used in diesel eng...
 4.4.70: The paper Microwave Obsevations of Daily Antarctic SeaIce Edge Expa...
 4.4.71: A consumer is trying to decide between two longdistance calling pl...
 4.4.72: Evaluate the following: a. (6) b. (5/2) c. F(4; 5) (the incomplete ...
 4.4.73: Let X have a standard gamma distribution with 7. Evaluate the follo...
 4.4.74: Suppose the time spent by a randomly selected student who uses a te...
 4.4.75: Suppose that when a transistor of a certain type is subjected to an...
 4.4.76: The special case of the gamma distribution in which is a positive i...
 4.4.77: A system consists of five identical components connected in series ...
 4.4.78: If X has an exponential distribution with parameter , derive a gene...
 4.4.79: a. The event {X2 y} is equivalent to what event involving X itself?...
 4.4.80: The lifetime X (in hundreds of hours) of a certain type of vacuum t...
 4.4.81: The lifetime X (in hundreds of hours) of a certain type of vacuum t...
 4.4.82: Let X the time (in 101 weeks) from shipment of a defective product ...
 4.4.83: Let X have a Weibull distribution with the pdf from Expression (4.1...
 4.4.84: a. In Exercise 72, what is the median lifetime of such tubes? [Hint...
 4.4.85: The authors of the paper from which the data in Exercise 1.27 was e...
 4.4.86: The article On Assessing the Accuracy of Offshore Wind Turbine Reli...
 4.4.87: Let X the hourly median power (in decibels) of received radio signa...
 4.4.88: a. Use Equation (4.13) to write a formula for the median ~ of the l...
 4.4.89: A theoretical justification based on a certain material failure mec...
 4.4.90: The article The Statistics of Phytotoxic Air Pollutants (J. Royal S...
 4.4.91: What condition on and is necessary for the standard beta pdf to be ...
 4.4.92: Suppose the proportion X of surface area in a randomly selected qua...
 4.4.93: Suppose the proportion X of surface area in a randomly selected qua...
 4.4.94: Stress is applied to a 20in. steel bar that is clamped in a fixed ...
 4.4.95: The accompanying normal probability plot was constructed from a sam...
 4.4.96: Consider the following ten observations on bearing lifetime (in hou...
 4.4.97: Construct a normal probability plot for the following sample of obs...
 4.4.98: The article A Probabilistic Model of Fracture in Concrete and Size ...
 4.4.99: Construct a normal probability plot for the fatiguecrack propagati...
 4.4.100: The article The LoadLife Relationship for M50 Bearings with Silico...
 4.4.101: Construct a probability plot that will allow you to assess the plau...
 4.4.102: The accompanying observations are precipitation values during March...
 4.4.103: Use a statistical software package to construct a normal probabilit...
 4.4.104: Let the ordered sample observations be denoted by y1, y2, . . . , y...
 4.4.105: The following failure time observations (1000s of hours) resulted f...
 4.4.106: Let X the time it takes a read/write head to locate a desired recor...
 4.4.107: A 12in. bar that is clamped at both ends is to be subjected to an ...
 4.4.108: Let X denote the time to failure (in years) of a certain hydraulic ...
 4.4.109: The completion time X for a certain task has cdf F(x) given by 0 x ...
 4.4.110: The breakdown voltage of a randomly chosen diode of a certain type ...
 4.4.111: The article Computer Assisted Net Weight Control (Quality Progress,...
 4.4.112: When circuit boards used in the manufacture of compact disc players...
 4.4.113: The article Characterization of Room Temperature Damping in Aluminu...
 4.4.114: The reaction time (in seconds) to a certain stimulus is a continuou...
 4.4.115: Let X denote the temperature at which a certain chemical reaction t...
 4.4.116: The article Determination of the MTF of Positive Photoresists Using...
 4.4.117: The article The Prediction of Corrosion by StatisticalAnalysis of C...
 4.4.118: A component has lifetime X that is exponentially distributed with p...
 4.4.119: The mode of a continuous distribution is the value x* that maximize...
 4.4.120: The article Error Distribution in Navigation (J. Institute of Navig...
 4.4.121: In some systems, a customer is allocated to one of two service faci...
 4.4.122: Suppose a particular state allows individuals filing tax returns to...
 4.4.123: Let Ii be the input current to a transistor and I0 be the output cu...
 4.4.124: The article Response of SiCf /Si3N4 Composites Under Static and Cyc...
 4.4.125: Let Z have a standard normal distribution and define a new rv Y by ...
 4.4.126: a. Suppose the lifetime X of a component, when measured in hours, h...
 4.4.127: In Exercises 111 and 112, as well as many other situations, one has...
 4.4.128: Based on data from a dartthrowing experiment, the article Shooting...
 4.4.129: The article Three Sisters Give Birth on the Same Day (Chance, Sprin...
 4.4.130: Let X denote the lifetime of a component, with f(x) and F(x) the pd...
 4.4.131: Let U have a uniform distribution on the interval [0, 1]. Then obse...
 4.4.132: Let U have a uniform distribution on the interval [0, 1]. Then obse...
 4.4.133: A function g(x) is convex if the chord connecting any two points on...
 4.4.134: Let X have a Weibull distribution with parameters 2 and . Show that...
 4.4.135: An individuals credit score is a number calculated based on that pe...
 4.4.136: Let V denote rainfall volume and W denote runoff volume (both in mm...
Solutions for Chapter 4: Continuous Random Variables and Probability Distributions
Full solutions for Probability and Statistics for Engineering and the Sciences (with Student Suite Online)  7th Edition
ISBN: 9780495382171
Solutions for Chapter 4: Continuous Random Variables and Probability Distributions
Get Full SolutionsProbability and Statistics for Engineering and the Sciences (with Student Suite Online) was written by and is associated to the ISBN: 9780495382171. Chapter 4: Continuous Random Variables and Probability Distributions includes 128 full stepbystep solutions. This expansive textbook survival guide covers the following chapters and their solutions. Since 128 problems in chapter 4: Continuous Random Variables and Probability Distributions have been answered, more than 20172 students have viewed full stepbystep solutions from this chapter. This textbook survival guide was created for the textbook: Probability and Statistics for Engineering and the Sciences (with Student Suite Online), edition: 7.

Acceptance region
In hypothesis testing, a region in the sample space of the test statistic such that if the test statistic falls within it, the null hypothesis cannot be rejected. This terminology is used because rejection of H0 is always a strong conclusion and acceptance of H0 is generally a weak conclusion

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

Biased estimator
Unbiased estimator.

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.

Chisquare test
Any test of signiicance based on the chisquare distribution. The most common chisquare tests are (1) testing hypotheses about the variance or standard deviation of a normal distribution and (2) testing goodness of it of a theoretical distribution to sample data

Conditional probability
The probability of an event given that the random experiment produces an outcome in another event.

Consistent estimator
An estimator that converges in probability to the true value of the estimated parameter as the sample size increases.

Continuous random variable.
A random variable with an interval (either inite or ininite) of real numbers for its range.

Continuous uniform random variable
A continuous random variable with range of a inite interval and a constant probability density function.

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 .

Correlation coeficient
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).

Defectsperunit control chart
See U chart

Design matrix
A matrix that provides the tests that are to be conducted in an experiment.

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

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

Expected value
The expected value of a random variable X is its longterm average or mean value. In the continuous case, the expected value of X is E X xf x dx ( ) = ?? ( ) ? ? where f ( ) x is the density function of the random variable X.

Finite population correction factor
A term in the formula for the variance of a hypergeometric random variable.

Fractional factorial experiment
A type of factorial experiment in which not all possible treatment combinations are run. This is usually done to reduce the size of an experiment with several factors.

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

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