D.1 Statistics and Probability
The largest theme in AI. Sampling techniques and bias, frequency distributions, central tendency and dispersion. Bivariate correlation, Pearson's r, regression. Probability — outcomes, complement, expected value, Venn and tree diagrams, conditional probability and independence. Discrete random variables, the binomial distribution, the normal distribution. Spearman's rank correlation. Hypothesis testing with χ² and t-tests.
Population, sampling, and biasSign up
Population vs sample · Sampling techniques and their biases · Outliers
Frequency distributions, histograms, cumulative frequency, box plotsSign up
Frequency tables and histograms · Cumulative-frequency S-curves · Quartiles and box plots
Central tendency and dispersionSign up
Mean, median, mode · Range, IQR, variance, standard deviation
Bivariate correlation and regressionSign up
Scatter plots and Pearson's r · Least-squares regression line · Predictions and reliability
Probability — outcomes, complement, expected valueSign up
Sample space and events · Complementary events · Expected value
Venn diagrams, tree diagrams, conditional probability, independenceSign up
Venn and tree diagrams · Conditional probability P(A|B) · Independence test
Discrete random variables and expected valueSign up
Probability distributions for discrete X · E(X) and Var(X)
Binomial distributionSign up
Conditions for binomial · Mean np, variance np(1−p) · GDC binomial calculations
Normal distributionSign up
Bell-curve properties · Z-scores and 68-95-99.7 rule · GDC inverse normal
Spearman's rank correlationSign up
Rank-based correlation · When to use rₛ vs r
Hypothesis testing — χ² and t-testsSign up
Null and alternative hypotheses · χ² goodness-of-fit and independence · Two-sample t-test on a GDC