CHAPTER 02
Probability Distributions
Probability Distributions
LEARNING PATH
Topics in this chapter
Read by topic; each article preserves the complete explanations, formulas, and tables from the original notes.
- 01→
Random Variables and Probability Density
Learn how random variables map outcomes to numbers and how PMFs, PDFs, and CDFs describe discrete and continuous probabilities.
46 content blocks - 02→
Degrees of Freedom
Understand degrees of freedom as independent information remaining after constraints and parameter estimation.
21 content blocks - 03→
Normal Distribution and Z Scores
Study the normal distribution, standardization, Z scores, cumulative probabilities, and links to other sampling distributions.
30 content blocks - 04→
Chi-Square Distribution
Build the chi-square distribution from sums of squared standard normal variables and connect it to variance inference.
35 content blocks - 05→
t Distribution
Learn standardization when the population standard deviation is unknown and how degrees of freedom control the tails.
24 content blocks - 06→
F Distribution
Construct the F distribution from a ratio of independent scaled chi-square variables and relate it to ANOVA and t tests.
36 content blocks - 07→
Exponential Distribution
Study waiting times under a constant event rate, memorylessness, survival functions, and the Poisson process.
33 content blocks - 08→
Binomial Distribution
Model success counts in independent repeated trials and derive the PMF, mean, variance, and normal approximation.
31 content blocks - 09→
Poisson Distribution
Model event counts in a fixed interval and connect the rate parameter to binomial limits and exponential waiting times.
35 content blocks