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Subject Syllabus

AL-302 - Probability and Statistics

AIML • SEMESTER-3

Course Modules

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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 random variables and their properties Distribution functions and densities Normal densities Exponential densities Gamma densities

Bivariate distributions and their properties Distribution of sums and quotients Conditional densities Bayes' rule

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

Curve fitting by the method of least squares Fitting of straight lines Fitting of second degree parabolas and more general curves Test of significance: Large sample test for single proportion Difference of proportions Single mean Difference of means Difference of standard deviations

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