Overview

Explore a comprehensive 9-hour course on statistical distributions, covering mean, variance, moments, and mode. Delve into various probability distributions, including Binomial, Normal, Poisson, Gamma, Beta, and more. Learn to derive moments, calculate means and variances, and understand the properties of different distributions. Study the Exponential Family, Method of Moments estimation, and specialized topics like truncated distributions and compound distributions. Gain practical skills in analyzing and interpreting statistical data through in-depth examinations of distribution characteristics and their applications in real-world scenarios.

Syllabus

Mean and Variance of a Binomial Distribution.
Mean and Variance of Logistic Distribution.
Variance of the sample variance.
Derive the moments of a Standard Normal Distribution.
Mean and Variance of Truncated Exponential Density.
Mean and Variance of Truncated Normal Density.
Mean and Variance of a Poisson Distribution.
Interesting Formula for the Sample Variance. U Statistics.
Mean and Variance of a Gamma Distribution.
Mean and Variance of a Discrete Uniform Distribution.
Mean and Variance of a Beta Distribution.
Mean and Variance of a Truncated Poisson Distribution.
Mean and Variance of a Cauchy Distribution.
Mean and Variance of a Log Normal Distribution.
Mean and Variance of a t Distribution.
Mean and Variance of an f Distribution.
Mode of a Binomial Distribution.
Mode of a Poisson Distribution.
Correlation of a Bivariate Discrete Distribution.
Moments of a Cauchy Distribution that are Finite.
LOTUS - Law of the Unconcious Statistician.
Mean, Variance, and CDF of Arcsine Distribution.
Mean and Variance Hypergeometric Distribution.
Mean and Variance of a Folded Normal Distribution.
Mean and Variance of a Compound Poisson Gamma Distribution.
Mean and Variance of a Double Exponential (Laplace) Distribution.
Mean, Variance, Median, and Mode of a Weibull Distribution.
Mean and Variance of a Beta Prime Distribution.
Mean and Variance of a General Beta Distribution.
Mean and Variance of a Chi Distribution.
Mean and Variance of a Truncated Cauchy Distribution.
Exponential Family: Mean and Variance.
Exponential Family: Normal Distribution.
Exponential Family: Bernoulli Distribution.
Exponential Family: Binomial Distribution (fixed n).
Exponential Family: Poisson Distribution.
Exponential Family: Negative Binomial Distribution (fixed r).
Exponential Family: Exponential Distribution.
Exponential Family: Pareto Distribution (known minimum).
Exponential Family: Weibull Distribution (known k).
Exponential Family: Laplace Distribution (known mean).
Exponential Family: Chi square Distribution.
Exponential Family: Gamma Distribution.
Exponential Family: Log Normal Distribution.
Exponential Family: Beta Distribution.
Exponential Family: Multinomial Distribution (fixed n).
Moments of a Normal Distribution.
Mean and Variance of a Non Central Chi square Distribution.
Mean, Variance, and Covariance of Quadratic Forms.
Mean, Variance, MGF, & CDF of a Gumbel Distribution.
Mean and Variance of a Beta Negative Binomial Distribution.
Marginal Distribution of a Poisson Gamma Mixture Distribution.
Method of Moments Estimation for a Beta Distribution (part 1).
Method of Moments and MLEs for a Beta Distribution (part 2).
Mean, Variance, and Covariance of a Dirichlet Distribution.
Mean and Variance of a Zero-Truncated Binomial Distribution.
Derive the MGF of a Logistic Distribution and use it to derive the Mean and Variance.
Find E(xlogx) for a Gamma Distribution.
Mean and Variance of an Inverse Gamma Distribution.
Method of Moments Estimators for an Inverse Gamma Distribution.
Mode of an F Distribution is less than One.
Mean and Variance Negative Binomial Distribution.
Mode of an Inverse Gamma Distribution.
Mean, Variance and Mode of a Half Normal Distribution.
Mean, Variance, and Method of Moments for a Two Parameter Lindley Distribution.
Mean, Variance, Median, and CDF of a Rayleigh Distribution.
CDF and Hazard Function for a Two Parameter Lindley Distribution.
Mean and Variance of a Beta Binomial Random Variable.
Method of Moments Estimation Beta Binomial Distribution.