Merge pull request #4 from sguda/patch-1

Chapter 3 R translation

ch3.R

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+####
+### probability4datascience chapter 3 R code translation
+### Translated by Sumeeth Guda
+####
+
+###
+# Libraries to import
+###
+
+library(ggplot2)
+library(tidyverse)
+
+##
+# Chapter 3.2
+##
+
+###
+# Histogram of the alphabets
+###
+
+f <- read.table('./ch3_data_english.txt')
+f <- f/100
+n <- c(1:26)
+ntag <- c('a','b','c','d','e','f','g','h','i','j','k','l','m',
+    'n','o','p','q','r','s','t','u','v','w','x','y','z')
+
+f$index <- n
+f$labels <- ntag
+
+barplot(f$V1~f$index, xaxt = 'n', xlab = "Letters", ylab = "Values") 
+axis(1, at=1:26, labels=ntag)
+
+
+###
+# Histogram of dice throw
+###
+q <- sample(1:6, 100, replace = T)
+
+hist(q + 0.5, 6)
+
+###
+# Histogram of an exponential random number
+###
+
+lambda <- 1
+k <- 1000
+set = runif(n=k, min=0, max=1)
+freq = -1/lambda * log(1-set)
+hist(freq, 200)
+
+###
+# Cross validation loss
+###
+lambda <- 1
+n <- 1000
+X <- runif(n=n, min=0, max=1)
+freq = -1/lambda * log(1-X)
+
+m <- c(5:200)
+J <- replicate(195, 0)
+
+for (i in 1:195) {
+    h <- n/m[i]
+    J[i] = (2/((n-1)*h)-((n+1)/((n-1)*h)))*sum((hist(freq, m[i])/n)^2)
+}
+
+plot(J, m)
+
+
+###
+# Mean of a vector unif(0,1)
+###
+X <- runif(n=10000, min=0, max=1)
+print(mean(X))
+
+###
+# Mean of a PMF value
+###
+p = c(0.25, 0.5, 0.25)
+x = c(0, 1, 2)
+EX = sum(p*x)
+print(EX)
+
+###
+# Mean of a geometric random variable
+###
+
+k = c(1:100)
+p = 0.5 ^ k
+EX = sum(p*k)
+print(EX)
+
+
+##
+# Chapter 3.5 Common discrete random variables
+##
+
+###
+# Bernouli random variables histogram
+###
+p <- 0.5
+n <- 1
+X <- rbinom(1000, n, p)
+hist(X)
+
+###
+# Binomial random variables histogram
+###
+
+p <- 0.5
+n <- 10
+X <- rbinom(5000, n, p)
+hist(X)
+
+###
+# Binomial CDF histogram
+###
+
+p <- 0.5
+n <- 10
+x <- 0:n
+plot(x, pbinom(x, size = n, prob = p), type="h")
+
+###
+# Poisson-Binomial Approximation
+###
+n <- 5000
+p <- 0.01
+x <- rbinom(10000, 5000, 0.01)
+pois <- ppois(n*p, x)
+plot(x, pois)
+
+
+###
+# Photon shot noise 
+###
+
+### Wasn't able to get the image processing packages to load in my dev environment.