Cumulant Generating Function | Cumulants of Probability Distribution | Statistics B.Sc. 3rd Year

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In this series, we will study about
Central moments, First four central moments in terms of raw moments and vise-versa. Karl Pearson's Beta and Gamma coefficients. The measure of skewness and kurtosis. Random experiment. Sample space, Event, Types of events, Probability, and Conditional probability of an event. Independent events, Theorems of the compound and total probabilities, Baye’s Theorem and its simple applications.
Random variable, discrete and continuous random variables, the Probability distribution of a discrete random variable, the Probability density function of a continuous random variable. Distribution functions, Mathematical expectation of a random variable and of a function of random variable, Moments and Moment generating function, Cumulant generating function and cumulants, Characteristic functions.
Discrete and continuous distributions with properties: Bernoulli, Binomial, Poisson, and Normal.
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