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Fundamental Theorem of Linear Algebra

5 minute read

Notation Let \(\mathfrak{B}=\{\mathbf{v}_1, \ldots, \mathbf{v}_n \} \text{ is a basis for } V.\) Define a function \([\cdot]_{\mathfrak{B}}:V \rightarr...

Distribution Function

2 minute read

Distribution Function Let $X$ be a random variable on $(\mathbb{R}, \mathcal{B}(\mathbb{R}), \mu)$. The distribution function (cumulative distribution functi...

Random Variable

less than 1 minute read

Measurable function Let $(E, \mathcal{E})$ and $(F, \mathcal{F})$ be measurable spaces where $E,F,$ are sets and $\mathcal{E}$ and $\mathcal{F}$ are $\sigma...

Probability Space

2 minute read

The sample space $\Omega$ is the set of all possible outcomes of an experiment. Points in $\omega \in \Omega$ are outcomes or realizations.