PROBABILITY

• Negative Version of Hypergeometric Distribution 20 Jul, 2021
• 4.8. Optional stopping theorem 22 Jan, 2021
• 4.5. Square integrable martingales 22 Jan, 2021
• 4.6.3. Riez's decomposition 21 Jan, 2021
• 4.6.2. Levy's theorem 21 Jan, 2021
• 4.6.1. Uniform integrability and convergence in $L^1$ 21 Jan, 2021
• 4.4. Martingale inequalities and convergence in $L^p$ 28 Dec, 2020
• 4.3. Application of martingales 28 Dec, 2020
• 4.2. Martingales and a.s. convergence 27 Dec, 2020
• 4.1. Conditional expectation 27 Dec, 2020
• 3.9. Infinitely divisible distributions 25 Dec, 2020
• 3.10. Limit theorems in ℝᵈ 23 Dec, 2020
• 3.6. Poisson convergence 23 Dec, 2020
• 3.4. Central limit theorem 23 Dec, 2020
• 3.3. Characteristic functions 22 Dec, 2020
• 3.2.2. Vague convergence and uniform tightness 22 Dec, 2020
• 3.2.1. Weak convergence 22 Dec, 2020
• 2.S1. Convergence concepts 21 Dec, 2020
• 2.5. Convergence of random series 21 Dec, 2020
• 2.4. Strong law of large numbers 21 Dec, 2020
• 2.3. Borel-Cantelli lemmas 20 Dec, 2020
• 2.2. Weak laws of large numbers 20 Dec, 2020
• 2.1. Independence 20 Dec, 2020
• 1.7. Product space 20 Dec, 2020
• 1.6. $L^p$ space 19 Dec, 2020
• 1.5. Convergence theorems and elementary inequalities 19 Dec, 2020
• 1.4. The Lebesgue integral 19 Dec, 2020
• 1.3. Random variables 18 Dec, 2020
• 1.2. Distributions 18 Dec, 2020
• 1.1. Basics on measure theory 18 Dec, 2020
• Application of Dynkin's π-λ theorem 13 May, 2020
• Kolmogorov's maximal inequality with shifted starting point 9 May, 2020
• Determination of random variables and random number generation 30 Apr, 2020
• Borel-Cantelli lemmas are converses of each other 29 Apr, 2020
• Irregularity of almost sure convergence 27 Apr, 2020
• Strong law of large numbers 25 Apr, 2020
• High-dimensional box 24 Apr, 2020