- 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 bulls-eye 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 multiple-choice 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 bulls-eye 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 six-sided 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 right-wing members and seven left-win...
- 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 bulls-eye 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 toll-free 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 right-handed and left-handed 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
Since 69 problems in chapter 3: Discrete Probability Distributions have been answered, more than 53403 students have viewed full step-by-step solutions from this chapter. Chapter 3: Discrete Probability Distributions includes 69 full step-by-step 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.
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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
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Additivity property of x 2
If two independent random variables X1 and X2 are distributed as chi-square with v1 and v2 degrees of freedom, respectively, Y = + X X 1 2 is a chi-square random variable with u = + v v 1 2 degrees of freedom. This generalizes to any number of independent chi-square random variables.
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Average
See Arithmetic mean.
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Bimodal distribution.
A distribution with two modes
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Bivariate distribution
The joint probability distribution of two random variables.
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C chart
An attribute control chart that plots the total number of defects per unit in a subgroup. Similar to a defects-per-unit or U chart.
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Categorical data
Data consisting of counts or observations that can be classiied into categories. The categories may be descriptive.
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Conditional probability density function
The probability density function of the conditional probability distribution of a continuous random variable.
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Continuous random variable.
A random variable with an interval (either inite or ininite) of real numbers for its range.
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Continuous uniform random variable
A continuous random variable with range of a inite interval and a constant probability density function.
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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).
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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 off-diagonal elements rij are the correlations between Xi and Xj .
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Cumulative distribution function
For a random variable X, the function of X deined as PX x ( ) ? that is used to specify the probability distribution.
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Curvilinear regression
An expression sometimes used for nonlinear regression models or polynomial regression models.
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Defect concentration diagram
A quality tool that graphically shows the location of defects on a part or in a process.
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Deining relation
A subset of effects in a fractional factorial design that deine the aliases in the design.
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Enumerative study
A study in which a sample from a population is used to make inference to the population. See Analytic study
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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.
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F-test
Any test of signiicance involving the F distribution. The most common F-tests 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.
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Finite population correction factor
A term in the formula for the variance of a hypergeometric random variable.