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Statistical Theory: Sum of Squared Normal mean=mu var=1 variables

"Best" predictors of Y using a function of X.

Alternative Formula for the Expected Value

Incomplete Beta Function as the Sum of Binomial Probabilities

CI for Population Median using Order Statistics

Discrete Order Statistics with Illustration using R

Sum of Poisson Probabilities equal a Chi-square Probability

Using R to Find an Exact CI for a Poisson Parameter

The Median Minimizes Absolute Loss. 3 proofs when X is continuous.

Markov Inequality. Chebyshev Inequality. Weak Law of Large Numbers.

Proof of Binomial Theorem with specific cases of the General Binomial Theorem

Big O, Little o Notation. Examples with Cumulant and Moment Generating Functions

Proof of Holm Bonferroni Correction Method

Proof of Simes Correction Method

2 formulas between the determinant, trace and eigen values of a matrix

Properties of the Gamma Function (part 1 of 2)

Properties of the Gamma Function (part 2 of 2)

Chi square approximation to an F Distribution

Asymptotic C I for the Difference of 2 Independent Population Means

Exact C I for the difference of 2 independent normal population means

1st 4 moments of the sample mean when x is a Bernoulli random variable

A df=1 noncentral chi sq distribution as a Poisson weighted mixture of central chi sq distributions

Using R: Calculating Probability for a Bivariate Normal Random Variable

Statistical Distance

Extended Cauchy-Schwarz Inequality

Rotational Invariance

Generating Double Exponential Data from Scratch

Kruskal's Proof of the Joint Distribution of the Sample Mean and Variance

Derive the CDF of an Inverse Gamma Distribution

Description:

Explore advanced statistical theory concepts through a comprehensive 5-hour video series. Delve into topics such as sum of squared normal variables, best predictors using functions, alternative expected value formulas, and incomplete beta functions. Learn about confidence intervals for population medians, discrete order statistics, and Poisson probabilities. Discover proofs for the median minimizing absolute loss, Markov and Chebyshev inequalities, and the weak law of large numbers. Study the binomial theorem, big O notation, and correction methods like Holm-Bonferroni and Simes. Examine matrix properties, gamma function characteristics, and distribution approximations. Investigate confidence intervals for population means, moments of sample means, and noncentral chi-square distributions. Gain practical skills using R for bivariate normal probability calculations and generating double exponential data. Explore statistical concepts such as rotational invariance, Kruskal's proof, and deriving cumulative distribution functions for inverse gamma distributions. Read more

Statistical Theory

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#Mathematics #Statistics & Probability #Programming #Domain-Specific Languages (DSL) #R Programming #Inequality #Data Science #Expected Values #Computer Science #Algorithms #Big O Notation #Probability Theory #Moment Generating Functions #Binomial Theorem

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