🔧
tool
相关软件（R代码）
```r # 演示中心极限定理 set.seed(123) # 从一个非正态分布（指数分布）中抽样 pop_data <- rexp(100000, rate = 1) # 指数分布，均值=1，方差=1 # 反复抽取样本，计算样本均值 sample_means <- replicate(10000, mean(sample(pop_data, size = 30))) # 可视化：原始分布 vs...
📖 定义
# 演示中心极限定理
set.seed(123)
# 从一个非正态分布（指数分布）中抽样
pop_data <- rexp(100000, rate = 1) # 指数分布，均值=1，方差=1
# 反复抽取样本，计算样本均值
sample_means <- replicate(10000, mean(sample(pop_data, size = 30)))
# 可视化：原始分布 vs 样本均值的抽样分布
par(mfrow = c(1, 2))
hist(pop_data, breaks = 100, main = "总体分布（指数分布）", xlab = "x", xlim = c(0, 5))
hist(sample_means, breaks = 50, main = "样本均值分布（n=30）", xlab = "样本均值",
freq = FALSE, xlim = c(0, 3))
# 叠加理论正态分布曲线
x_seq <- seq(0, 3, length.out = 100)
lines(x_seq, dnorm(x_seq, mean = 1, sd = 1/sqrt(30)), col = "red", lwd = 2)
legend("topright", legend = "理论正态分布", col = "red", lwd = 2)