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Getting started with react.js: basic concept of React component 1 What is React.js React, or React.js is an open source javascript framework from Facebook. React.js is ideal for doing view rendering work in large scale or single page application (SPA…

PDF version PDF & CDF The probability density function is $$f(x; \mu, \sigma) = {1\over\sqrt{2\pi}\sigma}e^{-{1\over2}{(x-\mu)^2\over\sigma^2}}$$ The cumulative distribution function is defined by $$F(x; \mu, \sigma) = \Phi\left({x-\mu\over\sigma}\ri…

PDF version PDF & CDF The probability density function of the uniform distribution is $$f(x; \alpha, \beta) = \begin{cases}{1\over\beta-\alpha} & \mbox{if}\ \alpha < x < \beta\\ 0 & \mbox{otherwise} \end{cases} $$ The cumulative distribu…

PDF version PDF & CDF The exponential probability density function (PDF) is $$f(x; \lambda) = \begin{cases}\lambda e^{-\lambda x} & x\geq0\\ 0 & x < 0 \end{cases}$$ The exponential cumulative distribution function (CDF) is $$F(x; \lambda) =…

PDF version PMF Suppose that a sample of size $n$ is to be chosen randomly (without replacement) from an urn containing $N$ balls, of which $m$ are white and $N-m$ are black. If we let $X$ denote the number of white balls selected, then $$f(x; N, m,…

PDF version PMF Suppose there is a sequence of independent Bernoulli trials, each trial having two potential outcomes called "success" and "failure". In each trial the probability of success is $p$ and of failure is $(1-p)$. We are obs…

PDF version PMF Suppose that independent trials, each having a probability $p$, $0 < p < 1$, of being a success, are performed until a success occurs. If we let $X$ equal the number of failures required, then the geometric distribution mass function…

PDF version PMF A discrete random variable $X$ is said to have a Poisson distribution with parameter $\lambda > 0$, if the probability mass function of $X$ is given by $$f(x; \lambda) = \Pr(X=x) = e^{-\lambda}{\lambda^x\over x!}$$ for $x=0, 1, 2, \cd…

PDF下载链接 PMF If the random variable $X$ follows the binomial distribution with parameters $n$ and $p$, we write $X \sim B(n, p)$. The probability of getting exactly $x$ successes in $n$ trials is given by the probability mass function: $$f(x; n, p) =…