Biostatistics Study NotesFrom concepts and derivations to interpretation

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.

9 topic articles
  1. 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
  2. 02

    Degrees of Freedom

    Understand degrees of freedom as independent information remaining after constraints and parameter estimation.

    21 content blocks
  3. 03

    Normal Distribution and Z Scores

    Study the normal distribution, standardization, Z scores, cumulative probabilities, and links to other sampling distributions.

    30 content blocks
  4. 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
  5. 05

    t Distribution

    Learn standardization when the population standard deviation is unknown and how degrees of freedom control the tails.

    24 content blocks
  6. 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
  7. 07

    Exponential Distribution

    Study waiting times under a constant event rate, memorylessness, survival functions, and the Poisson process.

    33 content blocks
  8. 08

    Binomial Distribution

    Model success counts in independent repeated trials and derive the PMF, mean, variance, and normal approximation.

    31 content blocks
  9. 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