Discussion 3

Part I.

Normal Distribution

mu <- 183.8
sigma <- 10.5
x <- seq(from = mu - 3*sigma,
         to = mu + 3*sigma,
         length.out = 9000)
pdf <- dnorm(x = x,
             mean = mu,
             sd = sigma)
plot(x = x,
     y = pdf,
     type = 'l',
     xlab = 'Density',
     ylab = 'Height',
     main = 'Normal Distribution of the Heights of Dutch Men')

Binomial Distribution

n <- 100
p <- 2/38
x <- 0:20
probabilities <- dbinom(x = x,
       size = n,
       prob = p)
barplot(height = probabilities,
        names.arg = x,
        col = "#79c36a",
        main = "Binomial Distribution of Roulette",
        xlab = "Number of Times Landing on Green",
        ylab = "Probability")

Poisson Distribution

n <- 10000
lambda <- 4.44
hist(rpois(n, lambda), 
           main = "Poisson Distributions of Concussions in High School Football", 
           xlab = "Number of Concussions", 
           ylab = "Frequency")

Part II.

Poisson:

n <- 40000 # total procedures
p <- .5 # probability of death from surgery
lambda <- (n * p) # mean
poisson <- rpois(10000, lambda)
hist(poisson)

Binomial:

binomial <- rbinom(10000, size = n, prob = p)
hist(binomial)