 3.3.1.1: Suppose that X B(10,0.12). Calculate: (a) P(X =3) (b) P(X =6) (c) P...
 3.3.1.2: Suppose that X B(7,0.8). Calculate: (a) P(X =4) (b) P(X =2) (c) P(X...
 3.3.1.3: Draw line graphs of the probability mass functions of a B(6,0.5) di...
 3.3.1.4: An archer hits a bullseye with a probability of 0.09, and the resu...
 3.3.1.5: A fair die is rolled eight times. Calculate the probability that th...
 3.3.1.6: A multiplechoice quiz consists of ten questions, each with ve poss...
 3.3.1.7: A u virus hits a company employing 180 people. Independent of the o...
 3.3.1.8: Consider the two independent binomial random variables X1 B(n1, p) ...
 3.3.1.9: A company receives 60% of its orders over the Internet. Within a co...
 3.3.1.10: When a company receives an order, there is a probability of 0.42 th...
 3.3.1.11: Investments are made in ten companies, and for each company there i...
 3.3.1.12: There is a probability of 0.93 that a visitor to a website will bou...
 3.3.2.1: If X has a geometric distribution with parameter p =0.7, calculate:...
 3.3.2.2: If X has a negative binomial distribution with parameters p =0.6 an...
 3.3.2.3: If X has a geometric distribution with parameter p =0.7, show thatE...
 3.3.2.4: Suppose that X1,...,Xr are independent random variables, each with ...
 3.3.2.5: Recall 3.1.4 where an archer hits a bullseye with a probability of...
 3.3.2.6: A supply container dropped from an aircraft by parachute hits a tar...
 3.3.2.7: Cards are chosen randomly from a pack of cards with replacement. Ca...
 3.3.2.8: When a sherman catches a sh, it is a young one with a probability o...
 3.3.2.9: Recall 3.1.9, in which a company receives 60% of its orders over th...
 3.3.2.10: Consider a fair sixsided die. The die is rolled until a 6 is obtai...
 3.3.2.11: A fair coin is tossed until the fth head is obtained. What is the p...
 3.3.2.12: ( 3.1.10 continued) A manager monitors orders that the company rece...
 3.3.2.13: Suppose that there is a probability of 0.65 that each of a series o...
 3.3.2.14: There is a probability of 0.93 that a visitor to a website will bou...
 3.3.3.1: Let X have a hypergeometric distribution with N =11, r =6, and n =7...
 3.3.3.2: A committee consists of eight rightwing members and seven leftwin...
 3.3.3.3: A box contains 17 balls of which 10 are red and 7 are blue. A sampl...
 3.3.3.4: A jury of 12 people is selected at random from a group of 16 men an...
 3.3.3.5: Five cards are selected at random from a pack of cards without repl...
 3.3.3.6: Consider a collection of N items of whichri are of type i, for 1i k...
 3.3.3.7: Thereare11itemsofaproductonashelfinaretailoutlet, andunknowntothecu...
 3.3.3.8: A plate has 15 cupcakes on it, of which 9 are chocolate and 6 are s...
 3.3.3.9: (a) Aboxcontains8redballsand8blueballs,and4balls are taken at rando...
 3.3.3.10: In a ground water contamination study, the researchers identify 25 ...
 3.3.3.11: An investor is considering making investments in ten companies. Unk...
 3.3.4.1: If X P(3.2), calculate: (a) P(X =1) (b) P(X 3) (c) P(X 6) (d) P(X =...
 3.3.4.2: If X P(2.1), calculate: (a) P(X =0) (b) P(X 2) (c) P(X 5) (d) P(X =...
 3.3.4.3: If X P(), show that E(X) = x=0 xP(X = x) = Also show that E(X2) E(X...
 3.3.4.4: The number of cracks in a ceramic tile has a Poisson distribution w...
 3.3.4.5: On average there are about 25 imperfections in 100 meters of optica...
 3.3.4.6: On average there are four trafc accidents in a city during one hour...
 3.3.4.7: Recall that the Poisson distribution with a parameter value of =npc...
 3.3.4.8: In a scanning process, the number of misrecorded pieces of informat...
 3.3.4.9: Suppose that the number of errors in a companys accounts has a Pois...
 3.3.4.10: ( 3.4.9 continued) What is the probability that there will be three...
 3.3.5.1: A garage sells three types of tires, type A, type B, and type C. A ...
 3.3.5.2: A fair die is rolled 15 times. Calculate the probability that there...
 3.3.5.3: Recall 3.1.4 and 3.2.5, where an archer hits a bullseye with a pro...
 3.3.5.4: A researcher plants 22 seedlings. After one month, independent of t...
 3.3.5.5: Recall 3.1.9 and 3.2.9, where a company receives 60% of its orders ...
 3.3.5.6: In a consumer satisfaction survey the responses are very unsatisfac...
 3.3.8.1: An integrated circuit manufacturer produces wafers that contain 18 ...
 3.3.8.2: A biologist has a culture consisting of 13 cells. In a period of 1 ...
 3.3.8.3: A beverage company has three different formulas for its soft drink ...
 3.3.8.4: A companys tollfree complaints line receives an average of about 4...
 3.3.8.5: The number of radioactive particles passing through a counter in on...
 3.3.8.6: In a typical sports playoff series, two teams play a sequence of ga...
 3.3.8.7: A golf shop sells both righthanded and lefthanded sets of clubs, ...
 3.3.8.8: Box A contains six red balls and ve blue balls. Box B contains ve r...
 3.3.8.9: Suppose that a box contains 40 items of which 4 are defective. If a...
 3.3.8.10: (a) If a fair die is rolled 22 times, what is the probability that ...
 3.3.8.11: A box contains 11 red balls and 8 blue balls. Six balls are taken a...
 3.3.8.12: Are the following statements true or false? (a) An unfair coin, for...
 3.3.8.13: (a) A fair die is rolled ten times. What is the probability of obta...
 3.3.8.14: The number of imperfections in an object has a Poisson distribution...
 3.3.8.15: A utility company calculates that there is a probability of 0.82 th...
 3.3.8.16: ( 3.8.15 continued) Suppose that eight problems are reported during...
Solutions for Chapter 3: Discrete Probability Distributions
Full solutions for Probability and Statistics for Engineers and Scientists  4th Edition
ISBN: 9781111827045
Solutions for Chapter 3: Discrete Probability Distributions
Get Full SolutionsSince 69 problems in chapter 3: Discrete Probability Distributions have been answered, more than 11720 students have viewed full stepbystep solutions from this chapter. Chapter 3: Discrete Probability Distributions includes 69 full stepbystep solutions. This 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.

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).

Addition rule
A formula used to determine the probability of the union of two (or more) events from the probabilities of the events and their intersection(s).

Asymptotic relative eficiency (ARE)
Used to compare hypothesis tests. The ARE of one test relative to another is the limiting ratio of the sample sizes necessary to obtain identical error probabilities for the two procedures.

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.

Axioms of probability
A set of rules that probabilities deined on a sample space must follow. See Probability

Bimodal distribution.
A distribution with two modes

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.

Counting techniques
Formulas used to determine the number of elements in sample spaces and events.

Defect concentration diagram
A quality tool that graphically shows the location of defects on a part or in a process.

Density function
Another name for a probability density function

Dependent variable
The response variable in regression or a designed experiment.

Discrete distribution
A probability distribution for a discrete random variable

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

Distribution free method(s)
Any method of inference (hypothesis testing or conidence interval construction) that does not depend on the form of the underlying distribution of the observations. Sometimes called nonparametric method(s).

Distribution function
Another name for a cumulative distribution function.

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.

Extra sum of squares method
A method used in regression analysis to conduct a hypothesis test for the additional contribution of one or more variables to a model.

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.

Fraction defective control chart
See P chart