https://gdpark.blog/series/basic-statistics-i-studied/Recent content in Basic Statistics I Studied on gdpark.blogHugoenSat, 28 Sep 2019 00:00:00 +0000https://gdpark.blog/posts/statistics-01-moment-generating-function/Mon, 13 Nov 2017 00:00:00 +0000https://gdpark.blog/posts/statistics-01-moment-generating-function/Turns out mean and variance are just the 1st and 2nd moments — and the MGF is the tool mathematicians built to pull any moment out, cleanly, anytime!https://gdpark.blog/posts/statistics-01-introduction/Sun, 12 Nov 2017 00:00:00 +0000https://gdpark.blog/posts/statistics-01-introduction/A casual dive into why sample variance divides by n-1 and how we use samples to estimate population parameters without measuring absolutely everyone.https://gdpark.blog/posts/statistics-02-derivation-of-the-poisson-distribution/Tue, 14 Nov 2017 00:00:00 +0000https://gdpark.blog/posts/statistics-02-derivation-of-the-poisson-distribution/We kick off the distributions series by deriving the Poisson from scratch — starting with the binomial and cranking n to infinity to see what shakes out.https://gdpark.blog/posts/statistics-03-derivation-of-the-exponential-distribution/Wed, 15 Nov 2017 00:00:00 +0000https://gdpark.blog/posts/statistics-03-derivation-of-the-exponential-distribution/We skip the normal distribution to derive the exponential distribution — aka the waiting time until the first event — straight from the Poisson!https://gdpark.blog/posts/statistics-04-derivation-of-the-gamma-distribution/Thu, 16 Nov 2017 00:00:00 +0000https://gdpark.blog/posts/statistics-04-derivation-of-the-gamma-distribution/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!!!!https://gdpark.blog/posts/statistics-05-derivation-of-the-chi-squared-distribution/Fri, 17 Nov 2017 00:00:00 +0000https://gdpark.blog/posts/statistics-05-derivation-of-the-chi-squared-distribution/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.https://gdpark.blog/posts/statistics-06-derivation-of-the-student-s-t-distribution/Sat, 18 Nov 2017 00:00:00 +0000https://gdpark.blog/posts/statistics-06-derivation-of-the-student-s-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.https://gdpark.blog/posts/statistics-07-derivation-of-the-f-distribution/Sat, 18 Nov 2017 00:00:00 +0000https://gdpark.blog/posts/statistics-07-derivation-of-the-f-distribution/We derive the F-distribution PDF from scratch — turns out it’s basically next of kin to the t-distribution — then wrap up with how to actually read an F-table.https://gdpark.blog/posts/statistics-08-hypothesis-testing/Tue, 21 Nov 2017 00:00:00 +0000https://gdpark.blog/posts/statistics-08-hypothesis-testing/A casual walkthrough of hypothesis testing basics — null vs. alternative hypotheses, Z-statistics, and how to decide when to reject what the data’s telling you.https://gdpark.blog/posts/statistics-09-a-hasty-conclusion/Tue, 21 Nov 2017 00:00:00 +0000https://gdpark.blog/posts/statistics-09-a-hasty-conclusion/Hastily wrapping up the stats fundamentals series because the math foundation got too shaky — no promises on when the next part’s coming, lol.https://gdpark.blog/posts/statistics-11-gauss-markov-theorem-and-the-proof-of-blue/Sun, 12 Nov 2017 00:00:00 +0000https://gdpark.blog/posts/statistics-11-gauss-markov-theorem-and-the-proof-of-blue/Digging into what OLS actually guarantees — the 5 assumptions behind linear regression and why they make your estimates BLUE according to the Gauss-Markov theorem.https://gdpark.blog/posts/statistics-12-python-poisson-exponential-and-gamma-distributions/Sun, 15 Sep 2019 00:00:00 +0000https://gdpark.blog/posts/statistics-12-python-poisson-exponential-and-gamma-distributions/Just plotted the Poisson, Exponential, and Gamma distributions in Python straight from Wikipedia’s parameters — skipped the random-variable cross-checks and kept it chill this time.https://gdpark.blog/posts/statistics-13-python-chi-squared-student-s-t-and-f-distributions/Sat, 28 Sep 2019 00:00:00 +0000https://gdpark.blog/posts/statistics-13-python-chi-squared-student-s-t-and-f-distributions/Wrapped up derivations of the chi-squared, t-, and F-distributions — and honestly it’s just reminded me how shaky my stats fundamentals still are lol.