Conditional probability. Independent events. Total probability. Bayes' theorem.
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☘ Lecture No 3: Combinatorics
Factorial and Gamma function. Multiplication rules. Linear and circular permutations.
Sampling. Newton binomial and multinomial formulae.
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☘ Lecture No 4: Univariate Discrete Random Variable
Basic definitions. Probability function and cumulative distribution function.
Mean, variance, and standard deviation.
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☘ Lecture No 5: Discrete Probability Distributions
Uniform, Bernoulli, binomial, geometric, negative binomial,
hypergeometric,
negative hypergeometric and Poisson distributions.
Stirling formula.
Asymptotic reductions of distributions.
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☘ Lecture No 6: Bivariate Discrete Random Variable
Joint probability function, marginal probability function.
Independent and correlated
random variables, covariance and correlation coefficient. Linear regression.
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☘ Lecture No 7: Univariate Continuous Random Variable
Probability density function and cumulative distribution function. Mean and variance.
Uniform, normal, exponential and Erlang distributions.
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☘ Lecture No 8: Central Limit Theorem
De Moivre—Laplace theorem, central limit theorem, and weak law of large numbers.