Exercise 3.18 (More Beta-Binomial)

# Load packages
library(bayesrules)

# Plot the Beta(3, 3) prior for pi
plot_beta(3, 3)

#plot_beta_binomial() y summarize_beta_binomial  con parametros (α=3,β=3) and data (y=30 of n=40) (Patrick)
plot_beta_binomial(alpha = 3, beta = 3, y = 30, n = 40)

summarize_beta_binomial(alpha = 3, beta = 3, y = 30, n = 40)

##       model alpha beta      mean      mode         var        sd
## 1     prior     3    3 0.5000000 0.5000000 0.035714286 0.1889822
## 2 posterior    33   13 0.7173913 0.7272727 0.004313639 0.0656783

#plot_beta_binomial() y summarize_beta_binomial  con parametros (α=3,β=3) and data (y=15 of n=20) (Harold)
plot_beta_binomial(alpha = 3, beta = 3, y = 15, n = 20)

summarize_beta_binomial(alpha = 3, beta = 3, y = 15, n = 20)

##       model alpha beta      mean      mode         var         sd
## 1     prior     3    3 0.5000000 0.5000000 0.035714286 0.18898224
## 2 posterior    18    8 0.6923077 0.7083333 0.007889546 0.08882312