 3.31: The random variable is the number of nonconforming solder connectio...
 3.32: In a voice communication system with 50 lines, the random variable ...
 3.33: An electronic scale that displays weights to the nearest pound is u...
 3.34: A batch of 500 machined parts contains 10 that do not conform to cu...
 3.35: A batch of 500 machined parts contains 10 that do not conform to cu...
 3.36: The random variable is the moisture content of a lot of raw materia...
 3.37: The random variable is the number of surface flaws in a large coil ...
 3.38: The random variable is the number of computer clock cycles required...
 3.39: An order for an automobile can select the base model or add any num...
 3.310: Wood paneling can be ordered in thicknesses of 18, 14, or 38 inch. ...
 3.311: A group of 10,000 people are tested for a gene called Ifi202 that h...
 3.312: In an acidbase titration, the milliliters of base that are needed ...
 3.313: The number of mutations in a nucleotide sequence of length 40,000 i...
 3.314: The sample space of a random experiment is {a, b, c, d, e, f }, and...
 3.315: For Exercises 315 to 318, verify that the following functions are...
 3.316: For Exercises 315 to 318, verify that the following functions are...
 3.317: For Exercises 315 to 318, verify that the following functions are...
 3.318: For Exercises 315 to 318, verify that the following functions are...
 3.319: An article in Knee Surgery, Sports Traumatology, Arthroscopy [Arthr...
 3.320: An optical inspection system is to distinguish among different part...
 3.321: In a semiconductor manufacturing process, three wafers from a lot a...
 3.322: The space shuttle flight control system called PASS (Primary Avioni...
 3.323: A disk drive manufacturer sells storage devices with capacities of ...
 3.324: Marketing estimates that a new instrument for the analysis of soil ...
 3.325: The distributor of a machine for cytogenics has developed a new mod...
 3.326: An assembly consists of two mechanical components. Suppose that the...
 3.327: An assembly consists of three mechanical components. Suppose that t...
 3.328: The data from 200 endothermic reactions involving sodium bicarbonat...
 3.329: Actual lengths of stay at a hospitals emergency department in 2009 ...
 3.330: The distribution of the time until a Web site changes is important ...
 3.331: The following table shows the typical depth (rounded to the nearest...
 3.332: Determine the cumulative distribution function of the random variab...
 3.333: Determine the cumulative distribution function for the random varia...
 3.334: Determine the cumulative distribution function for the random varia...
 3.335: Determine the cumulative distribution function for the random varia...
 3.336: Determine the cumulative distribution function for the random varia...
 3.337: Determine the cumulative distribution function for the random varia...
 3.338: Determine the cumulative distribution function for the variable in ...
 3.339: Determine the cumulative distribution function for the variable in ...
 3.340: Errors in an experimental transmission channel are found when the t...
 3.341: Errors in an experimental transmission channel are found when the t...
 3.342: The thickness of wood paneling (in inches) that a customer orders i...
 3.343: Determine the cumulative distribution function for the random varia...
 3.344: Determine the cumulative distribution function for the random varia...
 3.345: Determine the cumulative distribution function for the random varia...
 3.346: Determine the cumulative distribution function for the random varia...
 3.347: If the range of X is the set {0, 1, 2, 3, 4} and P1X x2 0.2, determ...
 3.348: Determine the mean and variance of the random variable in Exercise ...
 3.349: Determine the mean and variance of the random variable in Exercise ...
 3.350: Determine the mean and variance of the random variable in Exercise ...
 3.351: Determine the mean and variance of the random variable in Exercise ...
 3.352: Determine the mean and variance of the random variable in Exercise ...
 3.353: Determine the mean and variance of the random variable in Exercise ...
 3.354: Determine the mean and variance of the random variable in Exercise ...
 3.355: he range of the random variable X is where x is unknown. If each va...
 3.356: In a NiCd battery, a fully charged cell is composed of nickelic hyd...
 3.357: The space shuttle flight control system called PASS (Primary Avioni...
 3.358: Trees are subjected to different levels of carbon dioxide atmospher...
 3.359: An article in the Journal of Database Management [Experimental Stud...
 3.360: Calculate the mean and variance for the random variable in Exercise...
 3.361: Calculate the mean and variance for the random variable in Exercise...
 3.362: Calculate the mean and variance for the random variable in Exercise...
 3.363: Calculate the mean and variance for the random variable in Exercise...
 3.364: Let the random variable X have a discrete uniform distribution on t...
 3.365: Let the random variable X have a discrete uniform distribution on t...
 3.366: Thickness measurements of a coating process are made to the nearest...
 3.367: Product codes of two, three, four, or five letters are equally like...
 3.368: The lengths of plate glass parts are measured to the nearest tenth ...
 3.369: Assume that the wavelengths of photosynthetically active radiations...
 3.370: The probability of an operator entering alphanumeric data incorrect...
 3.371: Suppose that X has a discrete uniform distribution on the integers ...
 3.372: Show that for a discrete uniform random variable X, if each of the ...
 3.373: The number of pages in a PDF document you create has a discrete uni...
 3.374: Suppose that ninedigit Social security numbers are assigned at ran...
 3.375: For each scenario described below, state whether or not the binomia...
 3.376: Let X be a binomial random variable with and Use the binomial table...
 3.377: Let X be a binomial random variable with and Calculate the followin...
 3.378: The random variable X has a binomial distribution with n 10 and p 0...
 3.379: The random variable X has a binomial distribution with n 10 and p 0...
 3.380: The random variable X has a binomial distribution with n 10 and p 0...
 3.381: Sketch the probability mass function of a binomial distribution wit...
 3.382: Determine the cumulative distribution function of a binomial random...
 3.383: Determine the cumulative distribution function of a binomial random...
 3.384: An electronic product contains 40 integrated circuits. The probabil...
 3.385: The phone lines to an airline reservation system are occupied 40% o...
 3.386: A multiplechoice test contains 25 questions, each with four answer...
 3.387: A particularly long traffic light on your morning commute is green ...
 3.388: Samples of rejuvenated mitochondria are mutated (defective) in 1% o...
 3.389: An article in Information Security Technical Report [Malicious Soft...
 3.390: Heart failure is due to either natural occurrences (87%) or outside...
 3.391: A computer system uses passwords that are exactly six characters an...
 3.392: A statistical process control chart example. Samples of 20 parts fr...
 3.393: Because not all airline passengers show up for their reserved seat,...
 3.394: This exercise illustrates that poor quality can affect schedules an...
 3.395: Consider the lengths of stay at a hospitals emergency department in...
 3.396: Consider the visits that result in leave without being seen (LWBS) ...
 3.397: Assume a Web site changes its content according to the distribution...
 3.398: Consider the endothermic reactions in Exercise 328. A total of 20 ...
 3.399: Suppose the random variable X has a geometric distribution with p 0...
 3.3100: Suppose the random variable X has a geometric distribution with a m...
 3.3101: Consider a sequence of independent Bernoulli trials with p 0.2. (a)...
 3.3102: Suppose that X is a negative binomial random variable with p 0.2 an...
 3.3103: The probability of a successful optical alignment in the assembly o...
 3.3104: In a clinical study, volunteers are tested for a gene that has been...
 3.3105: Assume that each of your calls to a popular radio station has a pro...
 3.3106: A player of a video game is confronted with a series of opponents a...
 3.3107: Heart failure is due to either natural occurrences (87%) or outside...
 3.3108: 26 letters (az) or 10 integers (09). Suppose there are 10,000 users...
 3.3109: A trading company has eight computers that it uses to trade on the ...
 3.3110: Assume that 20 parts are checked each hour and that X denotes the n...
 3.3111: A faulttolerant system that processes transactions for a financial...
 3.3112: In the process of meiosis, a single parent diploid cell goes throug...
 3.3113: Show that the probability density function of a negative binomial r...
 3.3114: Consider the endothermic reactions in Exercise 328. Assume indepen...
 3.3115: A Web site randomly selects among 10 products to discount each day....
 3.3116: Consider the visits that result in leave without being seen (LWBS) ...
 3.3117: Suppose X has a hypergeometric distribution with N 100, n 4, and K ...
 3.3118: Suppose X has a hypergeometric distribution with N 20, n 4, and K 4...
 3.3119: Suppose X has a hypergeometric distribution with N 10, n 3, and K 4...
 3.3120: A batch contains 36 bacteria cells and 12 of the cells are not capa...
 3.3121: A company employs 800 men under the age of 55. Suppose that 30% car...
 3.3122: Printed circuit cards are placed in a functional test after being p...
 3.3123: The analysis of results from a leaf transmutation experiment (turni...
 3.3124: A state runs a lottery in which six numbers are randomly selected f...
 3.3125: Magnetic tape is slit into halfinch widths that are wound into car...
 3.3126: (a) Calculate the finite population corrections for Exercises 3117...
 3.3127: Consider the visits that result in leave without being seen (LWBS) ...
 3.3128: Consider the nonfailed wells in Exercises 331. Assume that four w...
 3.3129: Suppose X has a Poisson distribution with a mean of 4. Determine th...
 3.3130: Suppose X has a Poisson distribution with a mean of 0.4. Determine ...
 3.3131: Suppose that the number of customers who enter a bank in an hour is...
 3.3132: The number of telephone calls that arrive at a phone exchange is of...
 3.3133: Astronomers treat the number of stars in a given volume of space as...
 3.3134: Data from www.centralhudsonlabs determined the mean number of insec...
 3.3135: In 1898 L. J. Bortkiewicz published a book entitled The Law of Smal...
 3.3136: The number of flaws in bolts of cloth in textile manufacturing is a...
 3.3137: When a computer disk manufacturer tests a disk, it writes to the di...
 3.3138: The number of cracks in a section of interstate highway that are si...
 3.3139: The number of surface flaws in plastic panels used in the interior ...
 3.3140: The number of failures of a testing instrument from contamination p...
 3.3141: The number of content changes to a Web site follows a Poisson distr...
 3.3142: The number of views of a page on a Web site follows a Poisson distr...
 3.3143: Let the random variable X be equally likely to assume any of the va...
 3.3144: Let X denote the number of bits received in error in a digital comm...
 3.3145: Batches that consist of 50 coil springs from a production process a...
 3.3146: An automated egg carton loader has a 1% probability of cracking an ...
 3.3147: A total of 12 cells are replicated. Freshly synthesized DNA cannot ...
 3.3148: A congested computer network has a 1% chance of losing a data packe...
 3.3149: A particularly long traffic light on your morning commute is green ...
 3.3150: The probability is 0.6 that a calibration of a transducer in an ele...
 3.3151: An electronic scale in an automated filling operation stops the man...
 3.3152: The probability that an eagle kills a jackrabbit in a day of huntin...
 3.3153: Traffic flow is traditionally modeled as a Poisson distribution. A ...
 3.3154: A shipment of chemicals arrives in 15 totes. Three of the totes are...
 3.3155: The probability that your call to a service line is answered in les...
 3.3156: Continuation of Exercise 3155. (a) What is the probability that yo...
 3.3157: Continuation of Exercise 3155. (a) What is the probability that yo...
 3.3158: The number of messages sent to a computer bulletin board is a Poiss...
 3.3159: The number of messages sent to a computer bulletin board is a Poiss...
 3.3160: The number of errors in a textbook follows a Poisson distribution w...
 3.3161: The probability that an individual recovers from an illness in a on...
 3.3162: Patient response to a generic drug to control pain is scored on a 5...
 3.3163: In a manufacturing process that laminates several ceramic layers, 1...
 3.3164: Continuation of Exercise 3163. Determine the minimum number of ass...
 3.3165: Determine the constant c so that the following function is a probab...
 3.3166: A manufacturer of a consumer electronics product expects 2% of unit...
 3.3167: Messages that arrive at a service center for an information systems...
 3.3168: The random variable X has the following probability distribution: x...
 3.3169: Determine the probability mass function for the random variable wit...
 3.3170: Each main bearing cap in an engine contains four bolts. The bolts a...
 3.3171: Assume the number of errors along a magnetic recording surface is a...
 3.3172: An installation technician for a specialized communication system i...
 3.3173: From 500 customers, a major appliance manufacturer will randomly se...
 3.3174: It is suspected that some of the totes containing chemicals purchas...
 3.3175: Messages arrive to a computer server according to a Poisson distrib...
 3.3176: Flaws occur in the interior of plastic used for automobiles accordi...
 3.3177: Derive the convergence results used to obtain a Poisson distributio...
 3.3178: Show that the function f 1x2 in Example 35 satisfies the propertie...
 3.3179: Derive the formula for the mean and standard deviation of a discret...
 3.3180: Derive the expression for the variance of a geometric random variab...
 3.3181: An air flight can carry 120 passengers. A passenger with a reserved...
 3.3182: A company performs inspection on shipments from suppliers in order ...
 3.3183: A company performs inspection on shipments from suppliers in order ...
 3.3184: A manufacturer stocks components obtained from a supplier. Suppose ...
 3.3185: A large bakery can produce rolls in lots of either 0, 1000, 2000, o...
Solutions for Chapter 3: Discrete Random Variables and Probability Distributions
Full solutions for Applied Statistics and Probability for Engineers  5th Edition
ISBN: 9780470053041
Solutions for Chapter 3: Discrete Random Variables and Probability Distributions
Get Full SolutionsSince 185 problems in chapter 3: Discrete Random Variables and Probability Distributions have been answered, more than 22395 students have viewed full stepbystep solutions from this chapter. Chapter 3: Discrete Random Variables and Probability Distributions includes 185 full stepbystep solutions. This textbook survival guide was created for the textbook: Applied Statistics and Probability for Engineers, edition: 5. This expansive textbook survival guide covers the following chapters and their solutions. Applied Statistics and Probability for Engineers was written by and is associated to the ISBN: 9780470053041.

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.

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

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

Bayes’ theorem
An equation for a conditional probability such as PA B (  ) in terms of the reverse conditional probability PB A (  ).

Bias
An effect that systematically distorts a statistical result or estimate, preventing it from representing the true quantity of interest.

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.

Conditional mean
The mean of the conditional probability distribution of a random variable.

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.

Control chart
A graphical display used to monitor a process. It usually consists of a horizontal center line corresponding to the incontrol value of the parameter that is being monitored and lower and upper control limits. The control limits are determined by statistical criteria and are not arbitrary, nor are they related to speciication limits. If sample points fall within the control limits, the process is said to be incontrol, or free from assignable causes. Points beyond the control limits indicate an outofcontrol process; that is, assignable causes are likely present. This signals the need to ind and remove the assignable causes.

Cook’s distance
In regression, Cook’s distance is a measure of the inluence of each individual observation on the estimates of the regression model parameters. It expresses the distance that the vector of model parameter estimates with the ith observation removed lies from the vector of model parameter estimates based on all observations. Large values of Cook’s distance indicate that the observation is inluential.

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

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

Empirical model
A model to relate a response to one or more regressors or factors that is developed from data obtained from the system.

Enumerative study
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.

Fixed factor (or fixed effect).
In analysis of variance, a factor or effect is considered ixed if all the levels of interest for that factor are included in the experiment. Conclusions are then valid about this set of levels only, although when the factor is quantitative, it is customary to it a model to the data for interpolating between these levels.

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

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