We are to take 100 successive random samples (of 30 each) of a distribution other than normal and plot the distribution of the mean and of the minimu of these samples.

# Setting parameters

#Let n be the sample size, in this case, n = 30
#Let i be the number of iteration, in this case, i=100

# Let vector_mean be the repository of the mean for each sample, we will initial to empty vector
# Let vector_min be the repository of the minimum for each sample, we will initial to empty vector

n <- 30
i <- 100
vector_mean <- vector(mode="numeric", length=0)
vector_min  <- vector(mode="numeric", length=0)

#Note: we will use j as loop counter in the for loop

for (j in 1:i){
  t <- runif(n)     # get random uniform distribution with sample size = n
  t_mean <- mean(t) # find mean of distribution
  t_min <- min(t)   # find minimum of distribution

# store mean and mininum in appropriate variables
  vector_mean <- c(vector_mean, t_mean)
  vector_min <- c(vector_min, t_min)
}

We will now plot the means and the minimums obtained above against

library(ggplot2)
ggplot() + aes(vector_mean) + geom_histogram(color="blue", fill="light blue") + ggtitle("Distribution of the Means")
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

ggplot() + aes(vector_min) + geom_histogram(color="blue", fill="dark blue") + ggtitle("Distribution of the Minimums")
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

Conclusion

The distribution of the means is, in this case, somewhat normal. This would be expected by the Central Limit Theorem. We would have had better results with more iterations (500 or even a 1,000). The distribution of the minimums is highly concencentrated towards 0