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# Probability and Probability Distributions

## Overview

This course helps to understand the basic concepts concerned with probability, basic principles, permutations and combinations to probability, rules associated with probability, probability distribution in later chapters. concept of random variable, discrete and continuous random variables, expected value, variance and standard deviation of a random variable, expectation and variance of random variable in managerial decision making. Probability distribution, discrete and continuous probability distribution, discrete and continuous probability distribution, Binomial, Poisson and normal distributions, inferential statistics.

## Syllabus

### COURSE LAYOUT

Course Layout:
WEEK I
1. Definition of probability, classical and relative frequency approach to probability2. Axiomatic Approach to Probability3. Bayes theorem and its application
WEEK II 4. Expectation of a Random variable and its properties5. Moment generating functions, their properties and uses6. Discrete Uniform Distribution
WEEK III7. Bernoulli Distribution8. Binomial distribution9. Poisson Distribution
WEEK IV 10. Geometric Distribution11. Negative binomial distribution12. Continuous Random Variable and Probability Density Function
WEEK V13. Standard univariate continuous distributions and their properties14. Uniform distribution15. Gamma and Beta distributions
WEEK VI16. Normal Distribution17. Cauchy and logistic distributions18. Pareto Distribution
WEEK VII 19. Bivariate Discrete & Continuous Distribution, its PMF & PDF20. Bivariate moments and definition of raw and central product moments21. Marginal and conditional distributions
WEEK VIII 22. Conditional Mean and Conditional Variance23. Bivariate Normal Distribution (Part-I)24. Bivariate Normal Distribution (Part-Il)
WEEK IX 25. Practical – Computing probability using addition and multiplication theorem26. Conditional Probability and Independent Events27. Practical – Computing probability using conditional probability and Baye’s theorem
WEEK X28. Practical-Problems on PMF Variance, Expectation, Quartiles, Skewness and Kurtosis29. Sketching the probability distribution functions30. Practical-Computations of probabilities and fitting discrete distributions
WEEK XI 31. Sketching Distribution Functions and Density Functions32. Computation of probabilities, expectation, moments & moment generating functions33. Fitting Standard Univariate Continuous Distributions such as Normal and Exponential Distributions
WEEK XII 34. Simulation of Random Samples from Standard Univariate Continuous Distributions such as Normal, Exponential and Cauchy Distributions35. Computing Marginal and Conditional Probability Distributions36. Computing Marginal and Conditional Expectations37. Drawing random samples from Bivariate Normal distribution

Dr. P.NAGESH

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