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This code simulates Normal(0,1), and this visualization shows smaller samples can vary much more than large samples from the true distribution. Maybe it’s not a fascinating picture although there is a deep mystery or two in there. Can we know the truth? Isn’t everything we know based on a sample? Is everything we believe, like these three rnorm(), an incomplete story?

require(tidyverse)
require(tidyr)

random_simulations_1 <- tibble(rnorm(100000)) %>%
gather %>%
rename(distribution = key, observed = value)

random_simulations_2 <- tibble(rnorm(1000)) %>%
gather %>%
rename(distribution = key, observed = value) %>%
bind_rows(random_simulations_1)

random_simulations <- tibble(rnorm(10)#, rnorm(100)
#runif(100)#,
#rhyper(100, 100, 50, 10),
#rbinom(100, 10, .5)
) %>%
gather %>%
rename(distribution = key, observed = value) %>%
bind_rows(random_simulations_2)

# note we've repeated three times, time for a function
# also note there are other distributions to try this on
# and really, it may ne nice to simulate a few pulls of
#  the same size

ggplot(random_simulations, aes(observed,
fill = as.factor(distribution))) +
geom_density(alpha = 0.2) +
labs(title = "Simulate N(0,1)")