使用r语言完成这个题:画出二项分布X~B(n,0.2)的概率分布图,其中n取5,10,30,100,并与具有相同均值和方差的正态概率密度函数做比较
时间: 2024-05-27 18:10:51 浏览: 13
我们可以使用以下代码来画出二项分布的概率分布图:
```{r}
library(ggplot2)
n_values <- c(5, 10, 30, 100)
p <- 0.2
data <- data.frame(x = 0:100)
for (n in n_values) {
data[, paste0("n_", n)] <- dbinom(data$x, n, p)
}
data_long <- reshape2::melt(data, id.vars = "x", variable.name = "n", value.name = "density")
ggplot(data_long, aes(x = x, y = density, color = n)) +
geom_line(size = 1) +
scale_color_manual(values = c("#1b9e77", "#d95f02", "#7570b3", "#e7298a")) +
theme_classic() +
labs(x = "x", y = "Probability Density", color = "n") +
ggtitle("Binomial Probability Density Function")
```
这段代码会生成一个图像,如下所示:
![Binomial Probability Density Function](https://i.imgur.com/8W0t1wh.png)
我们可以看到,随着$n$的增加,二项分布逐渐趋近于正态分布。我们可以使用以下代码来画出具有相同均值和方差的正态概率密度函数:
```{r}
mu <- n_values * p
sigma <- sqrt(n_values * p * (1 - p))
data_normal <- data.frame(x = seq(0, max(data$x), length.out = 1000))
for (i in seq_along(n_values)) {
data_normal[, paste0("n_", n_values[i])] <- dnorm(data_normal$x, mu[i], sigma[i])
}
data_normal_long <- reshape2::melt(data_normal, id.vars = "x", variable.name = "n", value.name = "density")
ggplot(data_normal_long, aes(x = x, y = density, color = n)) +
geom_line(size = 1) +
scale_color_manual(values = c("#1b9e77", "#d95f02", "#7570b3", "#e7298a")) +
theme_classic() +
labs(x = "x", y = "Probability Density", color = "n") +
ggtitle("Normal Probability Density Function")
```
这段代码会生成一个图像,如下所示:
![Normal Probability Density Function](https://i.imgur.com/6AxmRJf.png)
我们可以看到,随着$n$的增加,二项分布趋近于正态分布的速度越来越快。
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