# Probability and Statistics

By
Chege, P. (Paul)
(2010)

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This module consists of three units: Unit 1: Descriptive Statistics and Probability Distributions Descriptive statistics in unit one is developed either as an extension of secondary mathematics or as an introduction to first time learners of statistics. It introduces the measures of dispersion in statistics. The unit also introduces the concept of probability and the theoretical treatment of probability. Unit 2: Random variables and Test Distributions This unit requires Unit 1 as a prerequisite. It develops from the moment and moment generating functions, Markov and Chebychev inequalities, special univariate distributions, bivariate probability distributions and analyses conditional probabilities. The unit gives insights into the analysis of correlation coefficients and distribution functions of random variables such as the Chi-square, t and F. Unit 3: Probability Theory This unit builds up from unit 2. It analyses probability using indicator functions. It introduces Bonferoni inequality random vectors,, generating functions, characteristic functions and statistical independence random samples. It develops further the concepts of functions of several random variables and independence of X and S2 in normal samples order statistics. The unit summarises with the treatment of convergence and limit theorems.