Probability and Statistics for Engineering and the Sciences

1. OVERVIEW AND DESCRIPTIVE STATISTICS. Populations, Samples, and Processes. Pictorial and Tabular Methods in Descriptive Statistics. Measures of Location. Measures of Variability. 2. PROBABILITY. Sample Spaces and Events. Axioms, Interpretations, and Properties of Probability. Counting Techniques. Conditional Probability. Independence. 3. DISCRETE RANDOM VARIABLES AND PROBABILITY DISTRIBUTIONS. Random Variables. Probability Distributions for Discrete Random Variables. Expected Values. The Binomial Probability Distribution. Hypergeometric and Negative Binomial Distributions. The Poisson Probability Distribution. 4. CONTINUOUS RANDOM VARIABLES AND PROBABILITY DISTRIBUTIONS. Probability Density Functions. Cumulative Distribution Functions and Expected Values. The Normal Distribution. The Exponential and Gamma Distributions. Other Continuous Distributions. Probability Plots. 5. JOINT PROBABILITY DISTRIBUTIONS AND RANDOM SAMPLES. Jointly Distributed Random Variables. Expected Values, Covariance, and Correlation. Statistics and Their Distributions. The Distribution of the Sample Mean. The Distribution of a Linear Combination. 6. POINT ESTIMATION. Some General Concepts of Point Estimation. Methods of Point Estimation. 7. STATISTICAL INTERVALS BASED ON A SINGLE SAMPLE. Basic Properties of Confidence Intervals. Large-Sample Confidence Intervals for a Population Mean and Proportion. Intervals Based on a Normal Population Distribution. Confidence Intervals for the Variance and Standard Deviation of a Normal Population. 8. TESTS OF HYPOTHESIS BASED ON A SINGLE SAMPLE. Hypotheses and Test Procedures. z Tests for Hypotheses About a Population Mean. The One-Sample t Test. Tests Concerning a Population Proportion. Further Aspects of Hypothesis Testing. 9. INFERENCES BASED ON TWO SAMPLES. z Tests and Confidence Intervals for a Difference between Two Population Means. The Two-Sample t Test and Confidence Interval. Analysis of Paired Data. Inferences Concerning a Difference betwee