###################################################################### # Field goal kicking example # # # ###################################################################### #n = 4, pi = 0.6, y = 2 dbinom(x = 2, size = 4, prob = 0.6) #n = 4, pi = 0.6, y = 0, 1, 2, 3, 4 dbinom(x = 0:4, size = 4, prob = 0.6) # CDF n = 4, pi = 0.6, y = 1 pbinom(q = 1, size = 4, prob = 0.6) sum(dbinom(x = 0:1, size = 4, prob = 0.6)) # Nice display data.frame(y = 0:4, fy = dbinom(x = 0:4, size = 4, prob = 0.6), Fy = pbinom(q = 0:4, size = 4, prob = 0.6)) # Plot n <- 4 y <- 0:n pi <- 0.6 plot(x = y, y = dbinom(x = y, size = n, prob = pi), type = "h", xlab = "y", ylab = "f(y)", main = "Plot of a binomial distribution for n = 4 and pi = 0.6", panel.first = grid(col = "gray", lty = "dotted"), lwd = 2, col = "red", ylim = c(0,0.4)) abline(h = 0) # Sample set.seed(8239) # Set a seed to reproduce result y <- rbinom(n = 10000, size = 4, prob = 0.6) # Take sample head(y) tail(y) # Frequencies and relative frequencies table(y) table(y)/length(y) # Histogram - bar placement is a little off due to the discreteness hist(y, main = "") # Better plot due to the discreteness save.count <- table(y) save.count barplot(height = save.count, names = c("0", "1", "2", "3", "4"), xlab = "y") # Compare to E(Y) and Var(Y) mean(y) var(y)