##### The binomial coefficient #####
factorial(5)
factorial(5)/(factorial(3)*factorial(5-3))
choose(5, 3)

##### The binomial distribution #####
dbinom(5, size = 10, prob = .22)
dbinom(5, prob = .22, size = 10)
dbinom(5, .22, 10)
d <- dbinom(0:10, size = 10, prob = .22)
d
sum(d)
100*round(d, digits = 3)
#pdf(file = "Lab7\\Lab7Barplot.pdf")
barplot(d, names = 0:10)
#dev.off()
sum(dbinom(0:2, size = 10, prob = .22))
pbinom(2, size = 10, prob = .22)
pbinom(6, size = 10, prob = .22)
sum(dbinom(7:10, size = 10, prob = .22))
pbinom(6, size = 10, prob = .22, lower.tail = F)

##### The normal distribution #####
pnorm(-1)
pnorm(0)
pnorm(2)

pnorm(2) - pnorm(1)
pnorm(-1) + (1 - pnorm(1))
2*pnorm(-1)

qnorm(.1)
qnorm(.1/2)

##### Cystic fibrosis crossover study #####
cf <- read.delim("http://myweb.uiowa.edu/pbreheny/161/data/cysticfibrosis.txt")
DrugBetter <- vector(length = nrow(cf))
for (i in 1:nrow(cf)) {
	if (cf$Drug[i] < cf$Placebo[i]) {
		DrugBetter[i] = 1
	} else {
		DrugBetter[i] = 0
	}
}

cf <- data.frame(cf, DrugBetter)

binom.test(sum(DrugBetter), length(DrugBetter))