수학/확률론

[Athreya] 8.1. Weak Laws of Large NumbersBy Palette_

$\def\NN{\mathbb{N}}$$\def\RR{\mathbb{R}}$$\def\eps{\epsilon}$$\def\calT{\mathcal{T}}$$\def\calP{\mathcal{P}}$$\def\calL{\mathcal{L}}$$\def\calR{\mathcal{R}}$$\def\calC{\mathcal{C}}$$\def\calF{\mathcal{F}}$$\def\calB{\mathcal{B}}$$\def\calS{\mathcal{S}}$$\def\calA{\mathcal{A}}$$\def\calG{\mathcal{G}}$$\newcommand{\inner}[2]{\langle#1, #2\rangle}$$\newcommand{\abs}[1]{\left\vert#1\right\vert}$$\n..

[Athreya] 7.2. Borel-Cantelli Lemmas, Tail $\sigma$-algebras, and Kolmogorov's 0-1 LawBy Palette_

$\def\NN{\mathbb{N}}$$\def\RR{\mathbb{R}}$$\def\eps{\epsilon}$$\def\calT{\mathcal{T}}$$\def\calP{\mathcal{P}}$$\def\calL{\mathcal{L}}$$\def\calR{\mathcal{R}}$$\def\calC{\mathcal{C}}$$\def\calF{\mathcal{F}}$$\def\calB{\mathcal{B}}$$\def\calS{\mathcal{S}}$$\def\calA{\mathcal{A}}$$\def\calG{\mathcal{G}}$$\newcommand{\inner}[2]{\langle#1, #2\rangle}$$\newcommand{\abs}[1]{\left\vert#1\right\vert}$$\n..

[Athreya] 7.1. Independent Events and Random VariablesBy Palette_

$\def\NN{\mathbb{N}}$$\def\RR{\mathbb{R}}$$\def\eps{\epsilon}$$\def\calP{\mathcal{P}}$$\def\calL{\mathcal{L}}$$\def\calR{\mathcal{R}}$$\def\calC{\mathcal{C}}$$\def\calF{\mathcal{F}}$$\def\calB{\mathcal{B}}$$\def\calS{\mathcal{S}}$$\def\calA{\mathcal{A}}$$\def\calG{\mathcal{G}}$$\newcommand{\inner}[2]{\langle#1, #2\rangle}$$\newcommand{\abs}[1]{\left\vert#1\right\vert}$$\newcommand{\norm}[1]{\lef..

[Athreya] 6.3. Kolmogorov's consistency theoremBy Palette_

$\def\NN{\mathbb{N}}$$\def\RR{\mathbb{R}}$$\def\eps{\epsilon}$$\def\calR{\mathcal{R}}$$\def\calC{\mathcal{C}}$$\def\calF{\mathcal{F}}$$\def\calB{\mathcal{B}}$$\def\calS{\mathcal{S}}$$\def\calA{\mathcal{A}}$$\newcommand{\inner}[2]{\langle#1, #2\rangle}$$\newcommand{\abs}[1]{\left\vert#1\right\vert}$$\newcommand{\norm}[1]{\left\Vert#1\right\Vert}$$\newcommand{\paren}[1]{\left(#1\right)}$$\newcomma..

[Athreya] 6.2. Random Variables and Random VectorsBy Palette_

$\def\NN{\mathbb{N}}$$\def\RR{\mathbb{R}}$$\def\eps{\epsilon}$$\def\calB{\mathcal{B}}$$\def\calS{\mathcal{S}}$ $\def\calA{\mathcal{A}}$$\newcommand{\inner}[2]{\langle#1, #2\rangle}$$\newcommand{\abs}[1]{\left\vert#1\right\vert}$$\newcommand{\norm}[1]{\left\Vert#1\right\Vert}$$\newcommand{\paren}[1]{\left(#1\right)}$$\newcommand{\sqbracket}[1]{\left[#1\right]}$$\def\var{\text{Var}}$$\def\cov{\tex..