Schaum's Easy Outlines: Probability and Statistics

APPENDIX E: 95th and 99th Percentile Values . . . 143

144 PROBABILITY AND STATISTICS

APPENDIX E: 95th and 99th Percentile Values . . . 145

Appendix F Values of e−λ 146 Copyright 2001 by the McGraw-Hill Companies, Inc. Click Here for Terms of Use.

APPENDIX F: Values of e−λ 147

Appendix G Random Numbers 148 Copyright 2001 by the McGraw-Hill Companies, Inc. Click Here for Terms of Use.

Index Alternative hypothesis, 86 Confidence level, 77 Areas under the standard normal Confidence limits, 77 Continuous probability distribu- curve, 136–37 Arithmetic mean, 15 tion, 35–37 Asymptotically normal, 53, 55 Continuous random variables, Basic probability, 1–13 34–41 Bayes’ theorem, 9 Correlation and dependence, 115– Bernoulli trials and distribution, 16 43–44 Covariance, 108 Best-fitting curve, 103 Critical values, 77 Beta distribution, 122–23 Curve fitting, regression, and cor- Beta function, 134 Binomial coefficients, 12 relation, 99–116 Binomial distribution, 43–44, Degrees of freedom, 124 52–55 Dependent variable, 102 Binomial expansion, 12 Descriptive statistics, 14–22 Deviation error, 102 Cauchy distribution, 121–22 Discrete probability distribution, Central limit theorem, 56 Centroid, 105 24–25 Chi-square distribution, 123–26, Discrete random variables, 23– 130–31, 140–41 33 Coefficient of determination, 112 Dispersion, 18, 39 Combinations, 11–12 Combinatorial analysis, 9 Elementary events, 3 Complementary error function, Empirical probability, 4, 74 Estimates 135 Conditional probability, 7–8 confidence interval, 76–84 Confidence intervals point and interval, 76 standard error, 110–11 differences and sums, 82–84 unbiased and efficient, 71, means, 78–80 population parameters, 76– 75–76 Estimation theory, 75–84, 97–98 77 Eulers’ formulas, 133 proportions, 81–82 Expected values, 27–28, 30, 38– 40 149 Copyright 2001 by the McGraw-Hill Companies, Inc. Click Here for Terms of Use.

150 PROBABILITY AND STATISTICS Factorial function, 133 Normal distribution, 45–51, 52– F distribution, 128–31, 142–45 54, 55, 88–89 Frequency distributions, 72–74 Null hypothesis, 86 Gamma distribution, 122 One-tailed tests, 90 Gamma function, 133 Gaussian distribution, 45–51 Parabola, 101 Generalized correlation coeffi- Percentiles, 20 Permutations, 10–11 cient, 114–15 Poisson distributions, 51–52, 54– Histogram, 73 55, 55 Hypergeometric distribution, Polygon graph, 73 Population and sample, 59, 60– 118 –21 Hypothesis and significance, 85– 61 Principle of counting, 10 98 Probability, 1–13, 35–37, 43, Independent events, 8–9 117– 31 Independent variable, 102 Probability distributions, 117–31 Interquartile range, 20–21 Product-moment formula, 113 Interval probability, 35 P Value, 90–93 Law of large numbers, 56–57 Quadratic curve, 101 Least-squares line, 104–10 Least-squares method, 102–04 Random experiments, 2 Level of significance, 87–88 Random numbers, 60, 148 Linear correlation coefficient, Random samples, 60–63 Random variables, 23–57 111–14 Region of acceptance, 89 Linear regression, 112 Region of nonsignificance, 89 Linear relationship, 100 Region of rejection, 89 Region of significance, 89 Mathematical topics, 132–35 Regression, 102 Mean, 15–16, 64–67 Reliability, 76 Measures of central tendency, 15 Measures of dispersion, 18 Sample mean, 64–67 Median, 16–17 Sample spaces and points, 2–3 Method of least squares, 102–04 Sample statistics, 61–63 Mode, 17 Sample variance, 71–72 Multinomial distribution, 118 Sampling distributions, 63–70 Sampling theory, 58–74 n factorial, 11 Scatter, 18, 39 Nonlinear relationship, 100

INDEX 151 Scatter diagram, 100–02 Theorems Skewness, 21–22 Bayes’, 9 Slope, 105 central limit, 56 Special integrals, 134–35 chi-square, 124–25 Special sums, 132 expectation, 30 Special tests, 93–97 F distribution, 129 Standard deviation, 18–19, 28– law of large numbers, 56–57 probability, 5–9 29 relationships among chi- Standard error, 63, 110–11 square, t, and F distribu- Standard normal curve, 46 tions, 130 Standard normal density function, sampling distribution of means, 64–67 45–46 Student’s t, 127, 130–31 Standard score, 46 variance, 30–33 Standard variable, 45 Statistical decisions, 85–86 Transformed variables, 102 Statistical hypothesis, 86 Translation of axes, 106 Stirling’s approximation to n!, Two-tailed tests, 90 Type I and Type II errors, 87 12–13, 134 Stirling’s asymptotic formula, 134 Unbiased estimate, 71, 75–76 Stochastic variable, 23 Uniform distribution, 121 Student’s t distribution, 126–28, Values of eϪl, 146 – 47 130–31, 138–39 Variance, 18–19, 28–29, 30–33, Sums of series, 132 38–40, 108 t distribution, see Student’s t dis- Variation, 112 tribution Test involving normal distribu- tion, 88–89 Test of hypothesis and signifi- cance, 85–98