---
title: "Jan25"
output: html_document
---

```{r setup, include=FALSE}
knitr::opts_chunk$set(echo = TRUE)
```

Similating the central limit theorem:



Normal data sample size 4

```{r}

n <- 4

data.norm <- matrix(rnorm(n*10000, mean=5, sd=2),
                    nrow=10000)
means.norm <- rowMeans(data.norm)
hist(means.norm, breaks=100, col="green", 
     prob=T)
lines(seq(0,10,by=0.01), 
      dnorm(seq(0,10, by=0.01), mean=5, sd=1),
      col="red", lwd=2)
lines(seq(0,10,by=0.01), 
      dnorm(seq(0,10, by=0.01), mean=5, sd=2))

```

Sample Size 25

```{r}
# Increase n to 25
n <- 25
data.norm <- matrix(rnorm(n*10000, mean=5, sd=2),
                    nrow=10000)
means.norm <- rowMeans(data.norm)
hist(means.norm, breaks=100, col="green", 
     prob=T)
lines(seq(0,10,by=0.01), 
      dnorm(seq(0,10, by=0.01), mean=5, sd=0.4),
      col="red", lwd=2)

```


Non-normal data: exponential

Sample size 4
```{r}
n <- 4
data.exp <- matrix(rexp(n*10000, 1),ncol=n)
means.exp <- rowMeans(data.exp)
hist(means.exp, breaks=100, col="green", 
     prob=T)
lines(seq(0,10,by=0.01), 
      dnorm(seq(0,10, by=0.01), mean=1, sd=0.5),
      col="red", lwd=2)


```

Sample size 25
```{r}
n <- 25
data.exp <- matrix(rexp(n*10000, 1),ncol=n)
means.exp <- rowMeans(data.exp)
hist(means.exp, breaks=100, col="green", 
     prob=T)
lines(seq(0,10,by=0.01), 
      dnorm(seq(0,10, by=0.01), mean=1, sd=0.2),
      col="red", lwd=2)
```

sample size 100
```{r}
n <- 100
data.exp <- matrix(rexp(n*10000, 1),ncol=n)
means.exp <- rowMeans(data.exp)
hist(means.exp, breaks=100, col="green", 
     prob=T)
lines(seq(0,10,by=0.01), 
      dnorm(seq(0,10, by=0.01), mean=1, sd=0.1),
      col="red", lwd=2)
```