|
Course Content
|
Introduction: Probability Spaces (Probability Spaces, Sigma Algebra, Event, Probability Gauge, Conditional Probability and Independence of Events), Probability Calculations, Random Variables, Intermittent and Continuous Random Variables, Distribution Functions, Some Properties of Distribution Function, Probability and Probability Density Functions, Discrete and Continuous Distributions. Expected Value: Expected Value of a Random Variable, Moments, Moment Extractor Function, Some Other Producer Functions, Skewness and Quadrature Coefficients, Expected Values of Linear Functions of Random Variables and Variances Multivariate Distributions: Vector Random Variables, Multivariate Distribution Functions, Conditional Distributions, Conditional Exponential Distributions, (Moment, Covariance and Correlation Concepts, Two Dimensional Normal Distribution Transformations: Functions of Random Variables, One Dimensional Transformations, Multidimensional Transformations, Jacobian Technique, Moment Extracting Function Technique Some Probability Distributions: Random Sampling, Sampling Distributions: Random Sampling, Sampling Distributions, Weighted Average, Log-normal, Cauchy), Continuous Distributions (Uniform, Exponential, Gamma, Chi-square, Beta, Estimation of the Mean and the Variance, Estimators of Confidence, Relative Ranges and Hypothesis Tests, Finding the Mean Approach of the Population Average, The Value of the P-Value and the Decision of the Simple Linear Regression and Correlation: Correlation between Two Variables, Simple Linear Regression, Estimation Regression Coefficients, Confidence Intervals and Hypothesis Tests.
|