Series
9 posts
Moment generating functions: raw moments, uniqueness of a distribution, and the product rule for sums of independent random variables.
Derive the Poisson probability formula from the binomial distribution, follow a handwritten one-page derivation, and plot probabilities with Python.
Derive the exponential waiting-time distribution from Poisson event counts, calculate its mean and variance with the moment generating function, and plot Python examples.
Deriving the Gamma distribution from scratch by connecting it to the Poisson process — turns out it's just waiting for the α-th event instead of the first!!!!
Chi-squared is just a gamma in disguise — we prove Z² follows it with 1 degree of freedom and show how sample variance ties in before jumping to the t-distribution.
Where the 'Student' name came from, why we ditch the Z-stat when σ is unknown, and a full derivation of the t-distribution PDF — plus properties and a worked example.
An introductory walkthrough of hypothesis tests, significance levels, p-values, power, and normal, t, and chi-square examples.
A hasty close to the basic statistics series: my math foundation felt too weak, and I don't know when I'll continue—or whether I'll keep blogging.