Name: Andrew ID: Collaborated with:

This lab is to be done in class (completed outside of class if need be). You can collaborate with your classmates, but you must identify their names above, and you must submit your own lab as an knitted HTML file on Canvas, by Sunday 10pm, this week.

## For reproducibility --- don't change this!

This week’s agenda: manipulating data objects; using built-in functions, doing numerical calculations, and basic plots; reinforcing core probabilistic ideas.

The binomial distribution

The binomial distribution \(\mathrm{Bin}(m,p)\) is defined by the number of successes in \(m\) independent trials, each have probability \(p\) of success. Think of flipping a coin \(m\) times, where the coin is weighted to have probability \(p\) of landing on heads.

The R function rbinom() generates random variables with a binomial distribution. E.g.,

rbinom(n=20, size=10, prob=0.5)

produces 20 observations from \(\mathrm{Bin}(10,0.5)\).

Some simple manipulations

Some simple plots

More binomials, more plots

Working with matrices

Warm up is over, let’s go big

Now let’s go really big

Going big with lists

big.bin.draws.mean = mean(big.bin.draws) = sd(big.bin.draws)
standardize = function(x) {
  return((x - big.bin.draws.mean) /
big.bin.draws.list.standardized.slow = lapply(big.bin.draws.list, standardize)
big.bin.draws.mean = mean(big.bin.draws) = sd(big.bin.draws)
standardize.slow = function(x) {
  return((x - mean(big.bin.draws)) / sd(big.bin.draws))
big.bin.draws.list.standardized.slow = lapply(big.bin.draws.list, standardize)