coin3 <- data.frame( N_Heads = c(0, 1, 2, 3), C_Heads = c(1, 3, 3, 1) ) attach(coin3) coin3$P_Heads <- C_Heads/sum(C_Heads)

options(repr.plot.width=7, repr.plot.height=4) barplot(coin3$P_Heads, names = coin3$N_Heads, main = "Discrete Probability Distribution of Flipping Three Coins")

barplot(prop.table(table(c('HHH', 'HHT', 'HHT', 'HTT', 'HHT', 'HTT', 'HTT', 'TTT'))), main = "Discrete Probability Distribution of Tossing Three Coins", xlab = "x = Number of Heads", ylab = "P(x)", col = "#6633FF")

attach(coin3) E_X = sum(N_Heads * P_Heads) E_X

Uniform_Random_Number <-runif(10000, -2, 1) hist(Uniform_Random_Number, probability = TRUE)

# Demonstration of Normal Distribution plotting options(repr.plot.width=7, repr.plot.height=4) x=seq(-4,4,length=200) y=1/sqrt(2*pi)*exp(-x^2/2) plot(x,y,type="l",lwd=2,col="red", main = "Normal Distribution")