simulation_law_of_large_number.R

# ---------- Law of Large Number ----------
# Install packages
install.packages('ggplot2')
library(ggplot2)
# Parameters
sample_mean = 100000
sample_size = 20
set.seed(1234)

# Uniform Distribution
x = runif(n = 4000, min = 0, max = 1)
hist(x)
mean(x)
sd(x)
# Resampling
dist = replicate(n = sample_mean,
                 expr = mean(sample(x = x,
                                    size = sample_size,
                                    replace = TRUE)))
hist(dist)
mean(dist)
sd(dist)
sd(x) / sqrt(sample_size) # Proven

# Means
mean(x)
means = cumsum(dist)/(1:sample_mean)
# Data viz
ggplot(data = data.frame(x = 1:sample_mean, 
                         y = means))+
  geom_line(aes(x = x,
                y = y),
            color = 'red',
            size = 1.5)+
  geom_hline(yintercept = mean(x))+
  labs(x = 'Number of observations',
       y = 'Cumulative mean')+
  theme_minimal()

# Variance
sd(x)
stdev = replicate(n = sample_mean,
                  expr = sd(sample(x = x,
                                   size = sample_size,
                                   replace = TRUE)))
mean(stdev)
variance = cumsum(stdev ^ 2)/(1:sample_mean)
# Data viz
ggplot(data = data.frame(x = 1:sample_mean, 
                         y = variance))+
  geom_line(aes(x = x,
                y = y),
            color = 'red',
            size = 1.5)+
  geom_hline(yintercept = mean(variance))+
  labs(x = 'Number of observations',
       y = 'Cumulative variance')+
  theme_minimal()