概率分布

随机抽样

sample(x, size, replace = FALSE, prob = NULL)

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sample(c("成功", "失败"), 10, replace = T, prob = c(0.9, 0.1))

排列组合与概率的计算

prod() 返回连乘积
choose() 返回取法的数目

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1/prod(52:49)
1/choose(52,49)

部分概率分布

二项分布：binom(n,p)

分布律：

$$f(x|n,p)=\begin{pmatrix}n\\x\end{pmatrix}p^x(1-p)^{n-x}$$

数字特征：$E(X)=np,var(X)=np(1-p)$

dbinom(x, size, prob, log = FALSE)

pbinom(q, size, prob, lower.tail = TRUE, log.p = FALSE)

qbinom(p, size, prob, lower.tail = TRUE, log.p = FALSE)

rbinom(n, size, prob)

正态分布：norm($\mu$,$\sigma^2$)

密度函数：

$$f(x|\mu,\sigma)=\frac{1}{\sqrt{2\pi}\sigma}e^{\frac{(x-\mu)^2}{2\sigma^2}}$$

数字特征：$E(X)=\mu,var(X)=\sigma^2$

dnorm(x, mean = 0, sd = 1, log = FALSE)

pnorm(q, mean = 0, sd = 1, lower.tail = TRUE, log.p = FALSE)

qnorm(p, mean = 0, sd = 1, lower.tail = TRUE, log.p = FALSE)

rnorm(n, mean = 0, sd = 1)

泊松分布：pois($\lambda$)

分布律：

$$f(x|\lambda)=\frac{\lambda^x}{x!}e^{-\lambda}$$

数字特征：$$E(X)=\lambda,var(X)=\lambda$$

dpois(x, lambda, log = FALSE)

ppois(q, lambda, lower.tail = TRUE, log.p = FALSE)

qpois(p, lambda, lower.tail = TRUE, log.p = FALSE)

rpois(n, lambda)

均匀分布：unif(a,b)

密度函数：

$$f(x|a,b)=\frac{1}{b-a}$$

数字特征：

$$E(X)=\frac{a+b}{2},var(X)=\frac{b^2-a^2}{12}$$

dunif(x, min = 0, max = 1, log = FALSE)

punif(q, min = 0, max = 1, lower.tail = TRUE, log.p = FALSE)

qunif(p, min = 0, max = 1, lower.tail = TRUE, log.p = FALSE)

runif(n, min = 0, max = 1)

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require(DAAG)
data(possum)
fpossum <- possum[possum$sex=="f", ]
var(fpossum$totlngth)
mad(fpossum$totlngth)^2