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Introduction to Random Experiments and Random Variables (Discrete and Continuous)
- Probability distribution, Properties and applicability
- Bernouli and discrete uniform distribution
Binomial, Poisson and Hypergeometric Distributions
- Binominal, Hypergeometric
- Poisson and geometric random variables, Identification and application of these distributions
Normal, Exponential, Gamma and Weibull Distributions
- Normal, Exponential, Gamma
- Weibull, Identification and application of these distributions
- Introduction and applicability, Student's distribution, Chi-square distribution and F-distribution
- Importance and application, Identification and appropriate distribution
Discrete distributions, Gaussian distribution, Linear models for regression, Regression with basis functions, Bias-variance, Bayesian regression, Bayesian model comparison, Evidence approximation, Probability, Conditional probability, Random variables and distributions, Independence, Expectation, Moment generating functions, Parametric families of distributions, Transformation of random variables, Order statistics, Sampling distributions under normality, Central limit theorem, Convergence concepts and illustrative applications.