Distributions and Simulation

Time Estimates:

Videos: 30-60 min

Readings: 10 min

Activities: 45 min

Check-ins: 3

Review: Statistical Distributions

Required Video: Review of Statistical Distributions

Optional Tutorial: Interactive Random Variable Creator

Simulating in R

Required Video: Simulating Data in R

Optional Reading: RProg Ch 20: Simulation

Check-In 1: The r, p, q, and d functions

Try to predict what the following outputs will be WITHOUT running the code in R. Drawing pictures of the relevant distributions may help.

(Yes, it is very easy to “cheat” on this question. But this is for your practice, and I recommend you give it some thought.)

## a
punif(0.674)

## b

pnorm(2)
qnorm(.975)

## c

pchisq(0, df = 12)

## d

qt(10, df = 16)

## e

dbinom(2, size = 2, prob = .4)
pbinom(1, size = 2, prob = .6)

Preparing for the Lab

The Central Limit Theorem

If you do not recall the Central Limit Theorem from you previous classes - or if you would benefit from a refresher:

Optional Video: The CLT

Check-In 2: The CLT

Explain the idea behind the CLT in your own words, using as little jargon/vocabulary as you can.

Plotting distributions

Here is the code that made one of the plots from the lecture video:

my_samples <- data.frame(x = rchisq(1000, df = 5))

ggplot(my_samples, aes(x)) + 
  geom_histogram(bins = 40, aes(y = ..density..), fill = "grey", col = "white") + 
  stat_function(fun= ~dchisq(.x, df = 5), col = "cornflowerblue", lwd = 2) +
  theme_classic()

Check-In 3: Plotting

Re-create this plot from the lecture slides: (The two colors are “cornflowerblue” and “deeppink”)