# STAT 134 (P2): Concepts of Probability (3 Units) 
# Spring 2013, UC Berkeley
#  
# The binomial distribution: Demonstration of convergence to the Normal distribution, empirical distribution, law of large numbers, and convergence to the Poisson distribution 
# Author:  Prof. Yun S. Song
# Date  :  February 7, 2013

setwd("DIRECTORY_NAME")  # Replace DIRECTORY_NAME with the directory on your computer that contains "binomial.R"
source("binomial.R")     # Loading the script

# Central Limit Theorem; convergence to the Normal distribution
plotBinDist(10,0.1)
plotBinDist(20,0.1)
plotBinDist(50,0.1,zoom=T)
plotBinDist(100,0.1,zoom=T)
plotBinDist(1000,0.1,zoom=T)

# Slower convergence
plotBinDist(10,0.01)
plotBinDist(20,0.01)
plotBinDist(50,0.01,zoom=T)
plotBinDist(100,0.01,zoom=T)
plotBinDist(1000,0.01,zoom=T)

# Fluctuation / Empirical distribution
sampleBin(50,0.1,1)       
sampleBin(50,0.1,10)
sampleBin(50,0.1,100)
sampleBin(50,0.1,1000)
sampleBin(50,0.1,10000)
sampleBin(50,0.1,100000)

# Law of large numbers  P(|#successes/n  - p| < epsilon)
# epsilon = 0.05      
LLN(10,0.1,10000,0.05)
LLN(100,0.1,10000,0.05)
LLN(1000,0.1,10000,0.05    
                  
# epsilon = 0.01      
LLN(10,0.1,10000,0.01)
LLN(100,0.1,10000,0.01)
LLN(1000,0.1,10000,0.01)
LLN(10000,0.1,10000,0.01)
LLN(20000,0.1,10000,0.01)

# Convergence to the Poisson distribution
plotBinDist(10,0.2,upper=10)
plotBinDist(100,0.02,upper=10)
plotBinDist(1000,0.002,upper=10)
plotBinDist(10000,0.0002,upper=10)
plotBinDist(100000,0.00002,upper=10)