Problem 2

n <- 1000
means <- rep(NA, n)  ## Means
sds <- rep(NA, n)  ## Standard deviations
x <- rnorm(n=n, mean=10, sd=6)
for (i in 1:n){
  means[i] <- mean(x[1:i])  ## mean of first i draws
  sds[i] <- sd(x[1:i])  ## sd for first i draws
  }
sds <- sds[!is.na(sds)]
mean(means)  ## Expected value of all cell 26 entries

## [1] 10.04

mean(sds)  

## [1] 5.859