Examples and illustration of basic statistic concepts, probability distribution, Monte Carlo simulation, preprocessing and visualization techniques, and statistical testing.
Concept |
Notebook |
Auto-correlation |
Link |
Entropy and Impurity |
Link |
Law of Large Number |
Link |
Central Limit Theorem |
Link |
Confidence Interval |
Link |
Gaussian Kernel |
Link |
Kernel Density Estimation |
Link |
Linear Regression |
Link |
Monte Carlo Integration |
Link |
Sum of Random Variables |
Link |
Taylor Expansion |
Link |
Universality of Uniform |
Link |
Name |
Notebook |
Common distributions |
Link |
Gaussian error function |
Link |
Integrating Gaussian |
Link |
Markove Inequality |
Link |
Name |
Notebook |
Smoothing time series |
Link |
Exponential smoothing time series |
Link |
Name |
Comments |
Notebook |
Matplotlib basics |
scatter, line chart, histogram, pie chart, subplots |
Link |
Seaborn basics |
scatter, violin-plot, pairwise correlation, heatmap |
Link |
Simulation Task |
Notebook |
Monty-Hall Problem: should I switch? |
Link |
Reservior Sampling |
Link |
Using 7-sided die to roll 1~10 with equal probability |
Link |
Using biased coin to similate unbiased coin |
Link |
Finding square root using Babylonian method |
Link |
Gender ratio of boy and girl |
Link |
Probability of same birthdays |
Link |
Combining normal distribution |
Link |
Conditional expectation |
Link |
Picking adjectives |
Link |
Recapture wild animals |
Link |
Probability of forming triangle |
Link |
Expected number of coin flips to get two heads |
Link |
Meaning of z-score |
Link |
Name |
Notebook |
t-test basic example (left, right, two-tail) |
Link |
t-test two-tailed (finches example) |
Link |
t-test paired sample one-tailed |
Link |
t-test paired sample two-tailed |
Link |
t-test two sample two-tailed |
Link |
Chi-square goodness of fit test |
Link |
Chi-square independence test |
Link |
Analysis of variance (ANOVA) |
Link |