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jmanton.wordpress.com | ||
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mkatkov.wordpress.com
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| | | | | For probability space $latex (\Omega, \mathcal{F}, \mathbb{P})$ with $latex A \in \mathcal{F}$ the indicator random variable $latex {\bf 1}_A : \Omega \rightarrow \mathbb{R} = \left\{ \begin{array}{cc} 1, & \omega \in A \\ 0, & \omega \notin A \end{array} \right.$ Than expected value of the indicator variable is the probability of the event $latex \omega \in... | |
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mathematicaloddsandends.wordpress.com
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| | | | | I recently learned of Craig's formula for the Gaussian Q-function from this blog post from John Cook. Here is the formula: Proposition (Craig's formula). Let $latex Z$ be a standard normal random variable. Then for any $latex z \geq 0$, defining $latex \begin{aligned} \mathbb{P}\{ Z \geq z\} = Q(z) = \dfrac{1}{\sqrt{2\pi}} \int_z^\infty \exp \left( -... | |
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almostsuremath.com
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| | | | | The monotone class theorem is a very helpful and frequently used tool in measure theory. As measurable functions are a rather general construct, and can be difficult to describe explicitly, it is common to prove results by initially considering just a very simple class of functions. For example, we would start by looking at continuous... | |
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blog.demofox.org
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| | | This article explains how these four things fit together and shows some examples of what they are used for. Derivatives Derivatives are the most fundamental concept in calculus. If you have a function, a derivative tells you how much that function changes at each point. If we start with the function $latex y=x^2-6x+13$, we can... | ||
