LEADER 04207nam 2200493 450 001 996418202203316 005 20211014135059.0 010 $a3-030-47479-8 024 7 $a10.1007/978-3-030-47479-9 035 $a(CKB)5590000000002318 035 $a(MiAaPQ)EBC6357782 035 $a(DE-He213)978-3-030-47479-9 035 $a(MiAaPQ)EBC6523230 035 $a(Au-PeEL)EBL6357782 035 $a(OCoLC)1198557787 035 $a(PPN)250222698 035 $a(EXLCZ)995590000000002318 100 $a20211014d2020 uy 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aPrimer for data analytics and graduate study in statistics /$fDouglas Wolfe, Grant Schneider 205 $a1st ed. 2020. 210 1$aCham, Switzerland :$cSpringer,$d[2020] 210 4$dİ2020 215 $a1 online resource (X, 233 p. 13 illus., 12 illus. in color.) 311 $a3-030-47478-X 327 $aIntro -- Preface -- Contents -- Chapter 1: Introduction -- Chapter 2: Basic Probability -- 2.1 Random Events and Probability Set Functions -- 2.2 Properties of Probability Functions -- 2.3 Conditional Probability -- 2.4 Exercises -- Chapter 3: Random Variables and Probability Distributions -- 3.1 Discrete Random Variables -- 3.2 Discrete Random Variables -- 3.3 Continuous Random Variables -- 3.4 Exercises -- Chapter 4: General Properties of Random Variables -- 4.1 Cumulative Distribution Function -- 4.1.1 Relationship Between c.d.f. and p.d.f -- 4.1.2 General Properties of a c.d.f. FX(x) -- 4.2 Median of a Probability Distribution -- 4.3 Symmetric Probability Distribution -- 4.4 Mathematical Expectations -- 4.5 Chebyshev´s Inequality -- 4.6 Exercises -- Chapter 5: Joint Probability Distributions for Two Random Variables -- 5.1 Joint Probability Distributions of Two Variables -- 5.1.1 Discrete Variables -- 5.1.2 Continuous Variables -- 5.2 Marginal Probability Distributions -- 5.3 Covariance and Correlation -- 5.4 Conditional Probability Distributions -- 5.5 Exercises -- Chapter 6: Probability Distribution of a Function of a Single Random Variable -- 6.1 Change of Variable Technique -- 6.2 Moment Generating Function Technique -- 6.3 Distribution Function Technique -- 6.4 Exercises -- Chapter 7: Sampling Distributions -- 7.1 Simple Random Samples -- 7.2 Sampling Distributions -- 7.3 General Approaches for Obtaining Sampling Distributions -- 7.3.1 Moment Generating Function Technique -- 7.3.2 Distribution Function Technique -- 7.3.3 Change of Variable Technique -- 7.4 Equal in Distribution Approach to Obtaining Properties of Sampling Distributions -- 7.5 Exercises -- Chapter 8: Asymptotic (Large-Sample) Properties of Statistics -- 8.1 Convergence in Probability -- 8.2 Convergence in Distribution -- 8.2.1 Convergence of Moment Generating Functions. 327 $a8.2.2 Central Limit Theorem (CLT) -- 8.2.3 Slutsky´s Theorem -- 8.2.4 Delta Method -- 8.3 Exercises -- Bibliography. 330 $aThis book is specially designed to refresh and elevate the level of understanding of the foundational background in probability and distributional theory required to be successful in a graduate-level statistics program. Advanced undergraduate students and introductory graduate students from a variety of quantitative backgrounds will benefit from the transitional bridge that this volume offers, from a more generalized study of undergraduate mathematics and statistics to the career-focused, applied education at the graduate level. In particular, it focuses on growing fields that will be of potential interest to future M.S. and Ph.D. students, as well as advanced undergraduates heading directly into the workplace: data analytics, statistics and biostatistics, and related areas. 606 $aMathematical statistics 615 0$aMathematical statistics. 676 $a519.5 700 $aWolfe$b Douglas A.$0613525 702 $aSchneider$b Grant 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996418202203316 996 $aPrimer for data analytics and graduate study in statistics$91905756 997 $aUNISA