https://www.xingchi.li/Xingchi's DomainA site for me to express ideas and thoughts on life and work. 2022-02-08T17:04:45-06:00 Xingchi Li https://www.xingchi.li/ Jekyll © 2022 Xingchi Li /assets/img/favicons/favicon.ico /assets/img/favicons/favicon-96x96.png Density of standard normal given sum larger than zero2021-10-13T15:21:00-05:00 2021-10-13T15:21:00-05:00 https://www.xingchi.li/posts/density-of-standard-normal-given-sum-larger-than-zero/ Anthony Li Question Given two i.i.d. standard normal random variables $X, Y$. What is the density of $X$ given $X+Y&gt;0$? Answer Find the probability of $X\le c$ given $X+Y&gt;0$. \begin{align}P(X\le c\vert X+Y&gt;0)&amp;=\frac{P(X\le c,Y&gt;-X)}{P(X+Y&gt;0)}\\&amp;=2\int_{-\infty}^c\int_{-X}^{+\infty}YdYdX\\&amp;=2\int_{-\infty}^c\Phi(X)dX\\&amp;=2\Phi(X)\phi(X)\end{align} Thus the density of \$... Force-directed graph layout2019-10-24T13:00:00-05:00 2021-07-28T15:13:34-05:00 https://www.xingchi.li/posts/force-directed-graph-layout/ Anthony Li Adding node labels: Show a node label (the node name, i.e., the source) on the top right of each node. If a node is dragged, its label must move with it. Styling edges: Style the edges based on the “value” field in the links array. Assign the following styles: If the value of the edge is equal to 0, the edge should be black, thin, and dashed. If the value of the edge is e...