Introduction to Probability and Statistics

Basic Probability Probability spaces conditional probability independence; Discrete random variables Independent random variables the multinomial distribution Poisson approximation to the binomial distribution infinite sequences of Bernoulli trials sums of independent random variables; Expectation of Discrete Random Variables Moments Variance of a sum Correlation coefficient Chebyshev's Inequality.

Continuous Probability Distributions Continuous random varibales and their properties distribution functions and densities normal exponential and gamma densities.

Bivariate Distributions Bivariate distributions and their properties distribution of sums and quotients conditional densities Bayes' rule.

Basic Statistics Measures of Central tendency Moments skewness and Kurtosis - Probability distributions Binomial Poisson and Normal - evaluation of statistical parameters for these three distributions Correlation and regression – Rank correlation.

Applied Statistics Curve fitting by the method of least squares- fitting of straight lines second degree parabolas and more general curves. Test of significance Large sample test for single proportion difference of proportions single mean difference of means and difference of standard deviations.

Small samples Test for single mean difference of means and correlation coefficients test for ratio of variances - Chi-square test for goodness of fit and independence of attributes.