Probability Distributions - Mean, Variance, MGF Derivation

Overview

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Explore a comprehensive video series that delves into the derivation of Mean, Variance, and Moment Generating Function (MGF) for various probability distributions. Learn how to calculate these essential statistical measures for distributions including Normal, Binomial, Bernoulli, Poisson, Uniform (Continuous), Hypergeometric, Negative Binomial, Geometric, Gamma, Exponential, Chi-Squared, Weibull, Log-Normal, Beta, Double Exponential, Student's t, and Discrete Uniform. Gain a deep understanding of probability theory and statistical analysis through step-by-step explanations and derivations presented in English, covering both discrete and continuous distributions.

Syllabus

Normal Distribution | Derivation of Mean, Variance & Moment Generating Function (MGF) in English.
Binomial Distribution - Derivation of Mean, Variance & Moment Generating Function in English.
Bernoulli Distribution - Derivation of Mean, Variance & Moment Generating Function (English).
Poisson Distribution - Derivation of Mean, Variance & Moment Generating Function in English.
Uniform Distribution (Continuous) - Derivation of Mean, Variance & Moment Gen. Function (in English).
HyperGeometric Distribution - Derivation of Mean and Variance (English).
Negative Binomial Distribution - Derivation of Mean, Variance & Moment Generating Function (English).
Geometric Distribution - Derivation of Mean, Variance & Moment Generating Function (English).
Gamma Distribution - Derivation of Mean, Variance & Moment Generating Function (MGF) (English).
Exponential Distribution - Derivation of Mean, Variance & Moment Generating Function (MGF) (English).
Chi Squared Distribution | Derivation of Mean, Variance & Moment Generating function (MGF) (English).
Weibull Distribution | Derivation of Mean, Variance & Moments (in English).
Log-Normal Distribution | Derivation of Mean, Variance & Moments (in English).
Beta Distribution | Derivation of Mean, Variance & MGF (in English).
Double Exponential Distribution | Derivation of Mean, Variance & MGF (in English).
Derivation of Moments of Normal Distribution.
Student's t Distribution: Derivation of Mean (in English).
Student's t Distribution: Derivation of Variance (in English).
Discrete Uniform Distribution Derivation of Mean (in English).
Discrete Uniform Distribution Derivation of Variance (in English).
Discrete Uniform Distribution Derivation of MGF (in English).
Discrete Uniform Distribution - Derivation of Mean, Variance, and MGF (Simple Version).