Probability & Statistics for Engineers I



Probability & Statistics for Engineers I


Course Outline: Introduction to Statistics: Concept of Data and Variables, Data Collection and Descriptive Statistics, Inferential Statistics, Populations and Samples; Descriptive Statistics: Frequency Tables and Graphs, Relative Frequency Tables and Graphs, Grouped Data, Histograms, Ogives, Stem and Leaf Plots, Sample Mean, Sample Median, Sample Mode, Sample Variance and Standard Deviation, Sample Percentiles and Box Plots, Chebyshev’s Inequality, Normal Data Sets, Paired Data Set and Sample Correlation Coefficient; Elements of Probability: Basic Terminology in Probability, Sample Space and Events, Venn Diagrams and Algebra of Events, Axioms of Probability, Conditional Probability, Bayes’ Theorem and Independent Events; Random Variables and Expectation: Random Variables, Types of Random Variables, Jointly Distributed Random Variables, Expectation, Property of Expected Values, Use of Expected Values in Decision Making, Variance, Covariance and Variance of Sums of Random Variables and Moment Generating Functions; Special Random Variables: Binomial Random Variables, Poisson Random Variables, Uniform Random Variables, Normal Random Variables, Exponential Variables, Gamma Distribution, Chi-Square Distribution, t-Distribution and F-Distribution; Distributions of Sampling Statistics: Central Limit Theorem, Sampling Distribution for Normal Population, and Sampling from a Finite Population; Parameter Estimation: Maximum Likelihood Estimators, Interval Estimates, Estimating the difference in Means of Two Normal Population, Approximate Confidence Interval for the Mean, Confidence Interval of the Mean of the Exponential Distribution and Bayes’ Estimator.