# Category:Probability Theory

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This category contains results about **Probability Theory**.

Definitions specific to this category can be found in Definitions/Probability Theory.

**Probability theory** is the branch of mathematics which studies probability spaces.

## Subcategories

This category has the following 84 subcategories, out of 84 total.

### A

- Addition Law of Probability (3 P)

### B

- Bayes' Factors (empty)
- Bayes' Theorem (9 P)
- Bernoulli Trials (empty)
- Bernoulli's Theorem (3 P)
- Bimodal Distributions (empty)
- Birthday Paradox (3 P)
- Bivariate Distributions (1 P)
- Bonferroni Inequalities (1 P)

### C

- Complementary Events (1 P)
- Compound Distributions (1 P)
- Conditional Probabilities (1 P)
- Continuous Probability Distributions (empty)

### D

- Degenerate Distribution (1 P)
- Dice (empty)
- Differential Entropy (3 P)
- Disjoint Events (1 P)

### E

- Examples of Uncertainty (2 P)

### G

- Gaussian Integral (1 P)

### H

### I

- Independent Events (7 P)

### J

### K

- Khinchin's Law (3 P)
- Kochen-Stone Theorem (2 P)
- Kolmogorov's Law (3 P)
- Kolmogorov-Sinai Entropy (2 P)

### L

- Law of Large Numbers (6 P)
- Lévy's Inversion Formula (3 P)

### M

- Markov's Inequality (2 P)
- Modes (1 P)

### O

### P

- Probability (1 P)
- Probability Mass Functions (1 P)
- Probability Measures (5 P)

### R

- Random Numbers (empty)

### S

- Standard Deviation (1 P)
- Statistical Physics (empty)
- Storage Theory (empty)

### T

- Total Probability Theorem (2 P)

### U

### V

## Pages in category "Probability Theory"

The following 80 pages are in this category, out of 80 total.

### B

### C

- Central Limit Theorem
- Characteristic Function of Random Variable is Well-Defined
- Characteristic Function on Event is Discrete Random Variable
- Classical Probability is Probability Measure
- Conditional Entropy Decreases if More Given
- Conditional Entropy Decreases if More Given/Corollary
- Conditional Entropy Given Trivial Sigma-Algebra is Entropy
- Conditional Entropy of Join as Sum
- Conditional Entropy of Join as Sum/Corollary 1
- Conditional Entropy of Join as Sum/Corollary 2
- Conditional Entropy of Join as Sum/Corollary 3
- Conditional Entropy of Join as Sum/Corollary 4
- Conditional Entropy of Join as Sum/Corollary 5
- Conditional Probability Defines Probability Space
- Countable Function on Power Set of Sample Space is Discrete Random Variable

### D

### E

### F

### G

### M

### P

- Probability Mass Function of Function of Discrete Random Variable
- Probability Measure is Monotone
- Probability Measure on Equiprobable Outcomes
- Probability Measure on Single-Subset Event Space
- Probability of Empty Event is Zero
- Probability of Event not Occurring
- Probability of Independent Events Not Happening/Corollary
- Probability of Limit of Sequence of Events
- Probability of Limit of Sequence of Events/Decreasing
- Probability of Limit of Sequence of Events/Increasing
- Probability of no 2 People out of 53 Sharing the Same Birthday
- Probability of Occurrence of At Least One Independent Event
- Probability of Set Difference of Events
- Product of Discrete Random Variables
- Product Rule for Probabilities
- Properties of Join
- Pullback Commutes with Generating Partition