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Probability Distributions
This paper is aimed at teaching the students various probability distributions which are useful in day to day life.
Random Variable: Definition and types of random variables. Probability mass function and Probability density function. Distribution function with properties (without proof). Joint, Marginal and Conditional probability distributions. Independence of two variable, definition and application of Jacobian transformation for one and two variables.
Expectation of a random variable and its simple properties. Addition and Multiplication theorems of Expectations. Variance and covariance and their properties.
Chebychev’s inequality with simple applications. Central moments and Non-central moments, Moment generating functions and their properties. Cumulant generating functions.
Bernoulli, Binomial, Poisson, Geometric Distribution with simple properties and applications. Fitting of Binomial and Poisson Distribution. Hypergeometric and Negative Binomial Distribution (examples, derivations, mean and variance) .
Rectangular, Normal,Fitting of Normal, Exponential, Cauchy, Gamma, Beta Distribution with properties.
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