## dbinom
dbinom(31, size=39, prob=0.7)
## Same as:
choose(39,31) * 0.7^31 * 0.3^8

## choose
## This is OK:
print(choose(39,31), digits=15)
print(factorial(39)/(factorial(31)*factorial(8)), digits=15)
## This is a problem:
print(choose(139,131), digits=15)
print(factorial(139)/(factorial(131)*factorial(8)), digits=15)

## pbinom
pbinom(31, size=39, prob=0.7)
## Same as:
sum(dbinom(0:31, size=39, prob=0.7))

## Plot of distribution
barplot(dbinom(0:39, 39, 0.7), names=0:39, border=FALSE)

## rbinom
x <- rbinom(100, size=39, prob=0.7)
x
barplot(table(x), border=FALSE)

## Finding p.u (picture)
f <- function(p) pbinom(31, 39, p)
p <- seq(0.85,1,0.01)
plot(p, f(p), type="l")
abline(h=0.025, col="red")

## uniroot
f.u <- function(p) pbinom(31, 39, p) - 0.025
uniroot(f.u, 0:1)$root

## uniroot part 2
f.l <- function(p) 1 - pbinom(30, 39, p) - 0.025
uniroot(f.l, 0:1)$root

## binom.test
binom.test(31,39)