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❯
Year 2
❯
Term 1
❯
A8 - Probability
❯
Theorems
Theorems
27 items under this folder.
Oct 01, 2026
01 - Implications Between Modes of Convergence
probability
probability-a8
Oct 01, 2026
02 - Convergence to a Constant in Distribution and Probability
probability
probability-a8
Oct 01, 2026
03 - Weak Law of Large Numbers
probability
probability-a8
Oct 01, 2026
04 - Markov's Inequality
probability
probability-a8
Oct 01, 2026
05 - Chebyshev's Inequality
probability
probability-a8
Oct 01, 2026
06 - Strong Law of Large Numbers
probability
probability-a8
Oct 01, 2026
07 - Central Limit Theorem
probability
probability-a8
Oct 01, 2026
08 - Properties of the Probability Generating Function
probability
probability-a8
Oct 01, 2026
09 - Uniqueness Theorem for Probability Generating Functions
probability
probability-a8
Oct 01, 2026
10 - Properties of the Moment Generating Function
probability
probability-a8
Oct 01, 2026
11 - Taylor Expansion of the Moment Generating Function
probability
probability-a8
Oct 01, 2026
12 - Uniqueness Theorem for Moment Generating Functions
probability
probability-a8
Oct 01, 2026
13 - Continuity Theorem for Moment Generating Functions
probability
probability-a8
Oct 01, 2026
14 - Change of Variables Formula for Joint Densities
probability
probability-a8
Oct 01, 2026
15 - Joint Distribution of a Markov Chain
probability
probability-a8
Oct 01, 2026
16 - Chapman-Kolmogorov Equations
probability
probability-a8
Oct 01, 2026
17 - Joint Distribution of a Markov Chain
probability
probability-a8
Oct 01, 2026
18 - Characterisation of Hitting Probabilities
probability
probability-a8
Oct 01, 2026
19 - Characterisation of Recurrence via Return Probabilities
probability
probability-a8
Oct 01, 2026
20 - Recurrence and Transience Are Class Properties
probability
probability-a8
Oct 01, 2026
21 - Characterisation of Mean Hitting Times
probability
probability-a8
Oct 01, 2026
22 - Existence and Uniqueness of Stationary Distributions
probability
probability-a8
Oct 01, 2026
23 - Convergence to Equilibrium
probability
probability-a8
Oct 01, 2026
24 - Ergodic Theorem
probability
probability-a8
Oct 01, 2026
25 - Time-Reversal of a Markov Chain
probability
probability-a8
Oct 01, 2026
26 - Balance Equations
probability
probability-a8
Oct 01, 2026
27 - Detailed Balance Implies Stationary
probability
probability-a8