---

title: “hhww22” author: “nivre_ix” date: “2025-04-21” output: html_document

 comp <- 15
 prob <- .20
 dbinom(4, size = comp, prob = prob)

## [1] 0.1876042

pbinom(4, size = comp, prob = prob)

## [1] 0.8357663

1 - pbinom(3, size = comp, prob = prob)

## [1] 0.3518379

1 - pbinom(4, size = comp, prob = prob)

## [1] 0.1642337

 expected <- comp * prob
 std_dev <- sqrt(comp * prob * (1 - prob))
 threshold <- expected + std_dev
 ceiling_thresh <- ceiling(threshold)
 1 - pbinom(ceiling_thresh - 1, size = comp, prob = prob)

## [1] 0.1642337

 phyper(7, m = 205, n = 195, k = 15) - phyper(6, m = 205, n = 195, k = 15)

## [1] 0.1938501

 phyper(7, m = 205, n = 195, k = 15)

## [1] 0.4600768

 dbinom(7, size = 15, prob = 205/400)

## [1] 0.190635

 pbinom(7, size = 15, prob = 205/400)

## [1] 0.4607811

 dnbinom(3, size = 2, prob = 0.5)

## [1] 0.125

 dgeom(2, prob = 0.5)

## [1] 0.125

 pbinom(9, size = 2000, prob = 0.002) - pbinom(5, size = 2000, prob = 0.002)

## [1] 0.2066469

 pbinom(8, size = 2000, prob = 0.002)

## [1] 0.9787556

  ppois(9, lambda = 4) - ppois(5, lambda = 4)

## [1] 0.2067374

  ppois(8, lambda = 4)

## [1] 0.9786366