 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 5919 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 Patricia 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.

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

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

Attribute
A qualitative characteristic of an item or unit, usually arising in quality control. For example, classifying production units as defective or nondefective results in attributes data.

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

Bivariate distribution
The joint probability distribution of two random variables.

Coeficient of determination
See R 2 .

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

Contour plot
A twodimensional graphic used for a bivariate probability density function that displays curves for which the probability density function is constant.

Correlation
In the most general usage, a measure of the interdependence among data. The concept may include more than two variables. The term is most commonly used in a narrow sense to express the relationship between quantitative variables or ranks.

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).

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

Critical region
In hypothesis testing, this is the portion of the sample space of a test statistic that will lead to rejection of the null hypothesis.

Cumulative normal distribution function
The cumulative distribution of the standard normal distribution, often denoted as ?( ) x and tabulated in Appendix Table II.

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.

Discrete random variable
A random variable with a inite (or countably ininite) range.

Error variance
The variance of an error term or component in a model.

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

Fisher’s least signiicant difference (LSD) method
A series of pairwise hypothesis tests of treatment means in an experiment to determine which means differ.

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
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