Explain Central Limit Theorem

Disclaimer

This notebook gives a graphical explanation of the central limit theorem and shows its consequences for quantitative genetics.

Sampling

Take a number of random numbers from the uniform distribution and sum them up. Repeat that for a given number of times and look at the distribution of the sums.

Example

n_nr_random_numbers <- 100
n_nr_repeat <- 1000
# draw 100 random numbers from uniform distributio
vec_random_numbers <- runif(n_nr_random_numbers)
# sum of random numbers
sum_random_numbers <- sum(vec_random_numbers) / n_nr_random_numbers

# repeat above 
rep_sum <- NULL
for (i in 1:n_nr_repeat){
  vec_random_numbers <- runif(n_nr_random_numbers)
  sum_random_numbers <- sum(vec_random_numbers) / n_nr_random_numbers
  rep_sum <- c(rep_sum, sum_random_numbers)
}
#rep_sum

hist(rep_sum)

Loops

# Output number 1 to 5
cat("1\n")

1

cat("2\n")

2

cat("3\n")

3

cat("4\n")

4

cat("5\n")

5

for (i in 1:5){
  cat(i, "\n")
}

1 
2 
3 
4 
5