## sheet 6, ex. 1

ppoisson <- function(k, lambda) {
	x <- exp(-lambda)
	if (k == 0) {
		return(x)
	}
	for (i in 1:k) {
		x <- (lambda/i)*x
	}
	return(x)
}

pgeometric <- function(k, p) {
	if (k == 0) {
		return(p)
	}
	x <- p
	if (k == 0) {
		return(x)
	}
	for (i in 1:k) {
		x <- p*x
	}
	return(x)
}

pnegbinom <- function(k, alpha, p) {
	x <- (1-p)^alpha
	if (k == 0) {
		return(x)
	}
	a <- p
	b <- (alpha-1)*a
	for (i in 1:k) {
		x <- (a+b/i)*x
	}
	return(x)
}

pbin <- function(k, n, p) {
	x <- (1-p)^n
	if (k == 0) {
		return(x)
	}
	a <- p/(p-1)
	b <- -(n+1)/a
	for (i in 1:k) {
		x <- (a+b/i)*x
	}
	return(x)
}