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clt_fun.R

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+# sampe n = 100 observations from the exponential distribution with mean = 5
+x <- data.frame(X = rexp(100, rate = 5))
+
+# plot it
+hist(x$X, main = "Exponential Distribution")
+abline(v= mean(x$X),col="red", lwd=5)
+
+datalist = list()
+# repeate this 120 times
+# I created a for loop to do this which repeats the line above 120 times
+for (i in 1:1200) {
+  # during each loop I create a variable x_1, x_2, etc. using the paste command
+  nam <- paste("x", i, sep = "_") 
+  # I create a list containing each of the 120 dataframes, each having 100 observations
+  datalist[[i]] = assign(nam, data.frame((rexp(100, rate = 5))))
+}
+
+# this syntax merges all of the list objects into one
+X100 <- do.call(cbind, datalist)
+
+# then I use the command "sapply" to compute the means of each column 
+# i.e., the mean of each 100 observations
+# sapply needs a data frame as input so before using sapply convert the list to a df
+X100_means <- data.frame(sapply(X100, FUN=mean))
+
+# the command "colnames" changes the name of the variable
+# here I am changing the fist variable name to "CLT_FUN" hence the [1]
+colnames(X100_means)[1] <- "CLT_FUN"
+
+# Now, if the CLT worked, this histogram of the mean of the means should be normal
+hist(X100_means$CLT_FUN)
+abline(v= mean(X100_means$CLT_FUN),col="red", lwd=5)
+