Mathematical Statistics with Applicatio...7th EditionDennis O. Wackerly Publisher: Cengage LearningISBN: 9781111798789
Mathematical Statistics with Applicatio...
Solutions for Mathematical Statistics with Applications
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Chapter 1 - What Is StatisticsChapter 1.1 - IntroductionChapter 1.2 - Characterizing A Set Of Measurements: Graphical MethodsChapter 1.3 - Characterizing A Set Of Measurements: Numerical MethodsChapter 2 - ProbabilityChapter 2.3 - A Review Of Set NotationChapter 2.4 - A Probabilistic Model For An Experiment: The Discrete CaseChapter 2.5 - Calculating The Probability Of An Event: The Sample-point MethodChapter 2.6 - Tools For Counting Sample PointsChapter 2.7 - Conditional Probability And The Independence Of Events
Chapter 2.8 - Two Laws Of ProbabilityChapter 2.9 - Calculating The Probability Of An Event: The Event-composition MethodChapter 2.10 - The Law Of Total Probability And Bayes’ RuleChapter 2.11 - Numerical Events And Random VariablesChapter 3 - Discrete Random Variables And Their Probability DistributionsChapter 3.2 - The Probability Distribution For A Discrete Random VariableChapter 3.3 - The Expected Value Of A Random Variable Or A Function Of A Random VariableChapter 3.4 - The Binomial Probability DistributionChapter 3.5 - The Geometric Probability DistributionChapter 3.6 - The Negative Binomial Probability Distribution (optional)Chapter 3.7 - The Hypergeometric Probability DistributionChapter 3.8 - The Poisson Probability DistributionChapter 3.9 - Moments And Moment-generating FunctionsChapter 3.10 - Probability-generating Functions (optional)Chapter 3.11 - Tchebysheff’s TheoremChapter 4 - Continuous Variables And Their Probability DistributionsChapter 4.2 - The Probability Distribution For A Continuous Random VariableChapter 4.3 - Expected Values For Continuous Random VariablesChapter 4.4 - The Uniform Probability DistributionChapter 4.5 - The Normal Probability DistributionChapter 4.6 - The Gamma Probability DistributionChapter 4.7 - The Beta Probability DistributionChapter 4.9 - Other Expected ValuesChapter 4.10 - Tchebysheff’s TheoremChapter 4.11 - Expectations Of Discontinuous Functions And Mixed Probability Distributions (optional)Chapter 5 - Multivariate Probability DistributionsChapter 5.2 - Bivariate And Multivariate Probability DistributionsChapter 5.3 - Marginal And Conditional Probability DistributionsChapter 5.4 - Independent Random VariablesChapter 5.6 - Special TheoremsChapter 5.7 - The Covariance Of Two Random VariablesChapter 5.8 - The Expected Value And Variance Of Linear Functions Of Random VariablesChapter 5.9 - The Multinomial Probability DistributionChapter 5.10 - The Bivariate Normal Distribution (optional)Chapter 5.11 - Conditional ExpectationsChapter 6 - Functions Of Random VariablesChapter 6.3 - The Method Of Distribution FunctionsChapter 6.4 - The Method Of TransformationsChapter 6.5 - The Method Of Moment-generating FunctionsChapter 6.6 - Multivariable Transformations Using Jacobians (optional)Chapter 7 - Sampling Distributions And The Central Limit TheoremChapter 7.2 - Sampling Distributions Related To The Normal DistributionChapter 7.3 - The Central Limit TheoremChapter 7.5 - The Normal Approximation To The Binomial DistributionChapter 8 - EstimationChapter 8.2 - The Bias And Mean Square Error Of Point EstimatorsChapter 8.4 - Evaluating The Goodness Of A Point EstimatorChapter 8.5 - Confidence IntervalsChapter 8.6 - Large-sample Confidence IntervalsChapter 8.7 - Selecting The Sample SizeChapter 8.8 - Small-sample Confidence Intervals For μ And Μ1 − Μ2Chapter 8.9 - Confidence Intervals For σ 2Chapter 9 - Properties Of Point Estimators And Methods Of EstimationChapter 9.2 - Relative EfficiencyChapter 9.3 - ConsistencyChapter 9.4 - SufficiencyChapter 9.5 - The Rao–blackwell Theorem And Minimum-variance Unbiased EstimationChapter 9.6 - The Method Of MomentsChapter 9.7 - The Method Of Maximum LikelihoodChapter 9.8 - Some Large-sample Properties Of Maximum-likelihoodChapter 10 - Hypothesis TestingChapter 10.2 - Elements Of A Statistical TestChapter 10.3 - Common Large-sample TestsChapter 10.4 - Calculating Type Ii Error Probabilities And Finding The Sample Size For Z TestsChapter 10.5 - Relationships Between Hypothesis-testing Procedures And Confidence IntervalsChapter 10.6 - Another Way To Report The Results Of A Statistical Test:attained Significance Levels, Or P-valuesChapter 10.8 - Small-sample Hypothesis Testing For μ And Μ1 − Μ2Chapter 10.9 - Testing Hypotheses Concerning VariancesChapter 10.10 - Power Of Tests And The Neyman–pearson LemmaChapter 10.11 - Likelihood Ratio TestsChapter 11 - Linear Models And Estimation By Least SquaresChapter 11.3 - The Method Of Least SquaresChapter 11.4 - Properties Of The Least-squares Estimators: Simple Linear RegressionChapter 11.5 - Inferences Concerning The Parameters ΒiChapter 11.6 - Inferences Concerning Linear Functions Of The Model Parameters: Simple Linear RegressionChapter 11.7 - Predicting A Particular Value Of Y By Using Simple Linear RegressionChapter 11.8 - CorrelationChapter 11.9 - Some Practical ExamplesChapter 11.10 - Fitting The Linear Model By Using MatricesChapter 11.12 - Inferences Concerning Linear Functions Of The Model Parameters: Multiple Linear RegressionChapter 11.13 - Predicting A Particular Value Of Y By Using Multiple RegressionChapter 11.14 - A Test For H0 : Βg+1 = Βg+2 = ··· = Βk =0Chapter 12 - Considerations In Designing ExperimentsChapter 12.2 - Designing Experiments To Increase AccuracyChapter 12.3 - The Matched-pairs ExperimentChapter 12.4 - Some Elementary Experimental DesignsChapter 13 - The Analysis Of VarianceChapter 13.2 - The Analysis Of Variance ProcedureChapter 13.4 - An Analysis Of Variance Table For A One-way LayoutChapter 13.5 - A Statistical Model For The One-way LayoutChapter 13.7 - Estimation In The One-way LayoutChapter 13.8 - A Statistical Model For The Randomized Block DesignChapter 13.9 - The Analysis Of Variance For A Randomized Block DesignChapter 13.10 - Estimation In The Randomized Block DesignChapter 13.11 - Selecting The Sample SizeChapter 13.12 - Simultaneous Confidence Intervals For More Than One ParameterChapter 13.13 - Analysis Of Variance Using Linear ModelsChapter 14 - Analysis Of Categorical DataChapter 14.3 - A Test Of A Hypothesis Concerning Specified Cell Probabilities: A Goodness-of-fit TestChapter 14.4 - Contingency TablesChapter 14.5 - R × C Tables With Fixed Row Or Column TotalsChapter 15 - Nonparametric StatisticsChapter 15.3 - The Sign Test For A Matched-pairs ExperimentChapter 15.4 - The Wilcoxon Signed-rank Test For A Matched-pairs ExperimentChapter 15.6 - The Mann–whitney U Test: Independent Random SamplesChapter 15.7 - The Kruskal–wallis Test For The One-way LayoutChapter 15.8 - The Friedman Test For Randomized Block DesignsChapter 15.9 - The Runs Test: A Test For RandomnessChapter 15.10 - Rank Correlation CoefficientChapter 16.2 - Bayesian Priors, Posteriors, And Estimators
Book Details
In their bestselling MATHEMATICAL STATISTICS WITH APPLICATIONS, premiere authors Dennis Wackerly, William Mendenhall, and Richard L. Scheaffer present a solid foundation in statistical theory while conveying the relevance and importance of the theory in solving practical problems in the real world. The authors' use of practical applications and excellent exercises helps you discover the nature of statistics and understand its essential role in scientific research.
Sample Solutions for this Textbook
We offer sample solutions for Mathematical Statistics with Applications homework problems. See examples below:
Calculation: Mean: The mean of a sample of measurements y1,y2,...,yn is defined as, y¯=1n∑i=1nyi....Chapter 1, Problem 22SEChapter 1, Problem 25SEChapter 2.4, Problem 19EChapter 2.5, Problem 34EChapter 2.6, Problem 51EChapter 2.6, Problem 68EChapter 2.7, Problem 77ETwo events A and B are said to be independent if any one of the below conditions is satisfied....
For any two events A and B, the addition rule of probability is P(A∪B)=P(A)+P(B)−P(A∩B). Substitute...Chapter 2.9, Problem 119ECalculation: Let A denote the event that the player wins the game, B denote a sum of i on first toss...Chapter 2, Problem 143SEChapter 2, Problem 144SEChapter 2, Problem 168SEChapter 3.2, Problem 11EChapter 3.3, Problem 15EChapter 3.3, Problem 33EChapter 3.4, Problem 55EChapter 3.4, Problem 61EChapter 3.4, Problem 63EChapter 3.5, Problem 85ECalculation: The mean for geometric random variable Y is, E(Y)=1p and variance is V(Y)=1−pp2. Also,...Calculation: The negative binomial distribution for a random variable Y is, p(y)=(y−1r−1)prqy−r,...Calculation: A hypergeometric probability distribution of random variable Y is,...Chapter 3.8, Problem 121ECalculation: The Poisson distribution with parameter λ for the random variable Y is, p(y)=λyy!e−λ,...Calculation: The geometric random variable Y has the probability distribution, p(y)=qy−1p ;...Chapter 3.11, Problem 169ECalculation: Mean: For a discrete random variable Y and probability function p(y), the expected...Calculation: Binomial distribution: A random variable Y is a binomial distribution based on n trails...Calculation: Consider the expression (ry)(N−rn−y)(Nn)....Calculation: A random variable Y is said to follow a Hypergeometric distribution, if the probability...The probability density function is obtained below: f(y)={0.2 −1≤y≤0,0.2+cy 0<y≤1,0, elsewhere...Chapter 4.3, Problem 33EChapter 4.4, Problem 48EThe mean volume of the particles is obtained below: The probability density function for the uniform...Chapter 4.5, Problem 58ECalculation: The value of z0 such that P(Z>z0)= 0.5 is obtained below: In general, the standard...It is given that X1 and X2 are two Poisson variables with means λ1 and λ2 respectively. Also it is...Note that a random variable is said to be a chi-square distribution with ν degrees of freedom if and...The random variable Y1 follows a binomial distribution with parameters n and p1. The probability...Chapter 4.9, Problem 142EThe density function of a random variable Y is given below: f(y)={2π(1+y2), −1≤y≤10 elsewhere. The...Let Y is a random variable whose density is a combination of two density function and it is defined...The expected value of Z2i−1 is as follows: E(Z2i−1)=∫−∞∞z2i−1f(z) dz=∫−∞∞12πz2i−1e(−12)z2dz Define...It is given that Y has a beta distribution with parameters α and β. The probability density function...Calculation: According to the given question using the range of Y1 and Y2, the required probability...Calculation: Consider that Y1 and Y2 are two continuous real valued random variables with joint...Calculation: Consider that Y1 and Y2 are two continuous real valued random variables with joint...Calculation: Consider that Y1 and Y2 are two continuous real valued random variables with joint...Calculation: Consider that Y1 and Y2 are two discrete real valued random variables. Then the joint...Calculation: Consider that Y1 and Y2 are two continuous real valued random variables with joint...Calculation: Consider that Y1 and Y2 are two random variables with means μ1 and μ2, respectively....Calculation: The possible values of Y1+Y2 are 1, 2, 3. Let Y=Y1+Y2. Using the fact that each of Y1...Calculation: Binomial probability distribution: A discrete random variable Y is said to follow a...Chapter 5, Problem 144SECalculation: Consider that Y1 and Y2 are two continuous real valued random variables with joint...Calculation: In Exercise 5.65 the joint density is given as follows:...Chapter 6.3, Problem 1ECalculation: From the given information, the probability density function for Y is f(y)=32y2,−1≤y≤1....Calculation: Gamma distribution: If the random variable X follows Gamma distribution with (α,β), The...Calculation: From the given information, Y1,Y2,...Yn are independent and identically distributed...Chapter 6.5, Problem 53EChapter 6, Problem 72SECalculation: From Theorem 6.5, the density function for kth order statistic, Y(k) is,...Calculation: From Theorem 6.5, the joint density function for Y(j) and Y(k) is,...Calculation: From Theorem 6.5, the joint density function for Y(j) and Y(k) is,...Calculation: From the given information, Y1 and Y2 are independent geometric random variables. The...Chapter 7.2, Problem 20EChapter 7.2, Problem 34EFrom the given information, X1,X2,............,Xk follows normal distribution with mean μi and...From the given information, Y follows binomial distribution and p=0.20. For n=5...Let p+3pq/n<1⇔3pq/n<1−p ⇔3pq/n<q ⇔pq/n<q3 Taking square on both sides...Chapter 7, Problem 88SEFrom the given information, X follows Poisson distribution with parameter λ and Y=(X−λ)/λ. The...Unbiased estimator: Consider that θ^ is point estimator of θ. The θ^ is said to be unbiased...Chapter 8.2, Problem 17EChapter 8.4, Problem 23EChapter 8.5, Problem 44EIt is given that Y1,Y2,Y3,Y4 have multinomial distribution with n trials and p1,p2,p3,p4 are the...Here, n1=31, n2=30, n3=26, and n4=28. The values of p1, p2, p3, and p4 are computed as follows:...Chapter 8.7, Problem 79EHere, μ1 is the mean of Population A and μ2 is the mean of Population B. The variance of two...Margin of error: In a confidence interval, the margin of error (E) denotes the range of values below...Consider two independent random samples of size n1 and n2 from the normal distribution with...The distribution for Y(n)=max(Y1,Y2,…,Yn) is given as follows:...It is known that the statistic (n−1)s2σ2 has chi-square distribution with n−1 degrees of freedom....It is given that Y1,Y2,...,Yn denote a random sample from the uniform distribution on the interval...It is given that Y1,Y2,...,Yn denote independent variables. The probability density function of each...Chapter 9.4, Problem 38EChapter 9.5, Problem 66ECalculation: The expectation of the given random variable Y is obtained as follows:...Chapter 9.7, Problem 85EThe density function of Rayleigh’s distribution is given as follows: f(y)={(2yθ)e−y2θ ; y>0,0 ;...Calculation: The expectation of the given random variable Y is obtained as follows:...Chapter 10.3, Problem 17EIt may be expected that there is no difference in the mean pre-test scores for students who were...The test hypotheses are given as follows: Denote μ1 as the mean verbal SAT scores for high school...Chapter 10.9, Problem 82EIn this context, Y1,Y2,...,Yn denote a random sample from the population that has the Poisson...In this context, Y1,Y2,...,Yn1 denotes a random sample from the population having normal...Chapter 10, Problem 115SEHere, it is known that the random variables X, Y, and W follow the normal distribution with the...Step-by-step procedure to obtain the graph: Mark the values of x along the horizontal axis from 1.5...It is given that the correlation between the variables X and Y is as follows: ρ=Cov(X,Y)σXσY It is...The statement is, if Model I is fit, the estimate for σ2 is based on 16 degrees of freedom. Model I...Chapter 11, Problem 95SEThe model is as follows: Y=β0+β1x1+β2x2+β3x3+ε From the given Table, the data can be formed into...A confidence interval measures the degree of uncertainty in a sampling method. It refers the...Calculation: Consider that k1,k2,k3 are the fractions of total number of observations that can be...Chapter 13.4, Problem 6EThe null and alternative hypotheses are as follows: Null hypothesis: There is no significant...It is known that MST=bk−1∑i=1k(Y¯i,.−Y¯)2. To find E(MST), it is required to find E(Y¯i,.2). The...There are n=bk experimental units available for comparing the effect of k treatments. A randomized...The formulas for sum of squares are as follows: TSS =∑i=1k∑j=1b(Yij−Y¯)2SST =b∑i=1k(Y¯i.−Y¯)2SSB...In this context, it is assumed that the assumptions associated with a multinomial experiment are all...Properties of a multinomial experiment: The experiment has n identical trials. The outcome of each...In this context, there are three classes n1,n2,n3, and n4 with corresponding probabilities...The hypotheses are given below: Null hypothesis: H0:p=0.5 Alternative hypothesis: Ha:p≠0.5 Consider,...Consider WA=∑i=1n1R(Ai)=∑i=1n1Xi Where, Xi={R(zi) if zi is from sample A0 if zi is from sample B If...
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