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statisticaloddsandends.wordpress.com | ||
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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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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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jaberkow.wordpress.com
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| | | | | Lately I have been making use of a continuous relaxation of discrete random variables proposed in two recent papers: The Concrete Distribution: A Continuous Relaxation of Discrete Random Variables and Categorical Reparameterization with Gumbel-Softmax. I decided to write a blog post with some motivation of the method, as well as providing some minor clarification on... | |
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cyclostationary.blog
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| | | Our toolkit expands to include basic probability theory. | ||