On Exercise 5, how about this (I'm rather new to R as well, so no guarantee
this is right and I'm sure there are more efficient ways to do this!):

fun1 <- function(x) {
  y <- 0
  for (i in 1:length(x))
      {y[i] <- (x[i]-mean(x))^2}
  sum(y)/(length(x)+1)
}

fun2 <- function(x) {
  y <- 0
  for (i in 1:length(x))
  {y[i] <- (x[i]-mean(x))^2}
  sum(y)/(length(x))
}

x <- rexp(15)
fun1(x)
fun2(x)

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