/* 

  Duck Hunter problem in Picat.

  From Siegrist "Probability Mathematical Statisics and Stochastic Processes", page 
  """
  Suppose that there are 5 duck hunters, each a perfect shot. A flock of 10 ducks fly over, and each
  hunter selects one duck at random and shoots. Find each of the following:
  1. The probability density function of the number of ducks that are killed.
  2. The mean of the number of ducks that are killed.
  3. The standard deviation of the number of ducks that are killed.
  """

  Cf my Gamble model gamble_duck_hunter_problem.rkt

  This program was created by Hakan Kjellerstrand, hakank@gmail.com
  See also my Picat page: http://www.hakank.org/picat/

*/

import ppl_distributions, ppl_utils.
import util.
% import ordset.

main => go.

/*
  var : num killed
  Probabilities:
  4: 0.4984000000000000
  5: 0.3056000000000000
  3: 0.1836000000000000
  2: 0.0122000000000000
  1: 0.0002000000000000
  mean = 4.097
  variance = 0.530391
  stdev = 0.728279

*/
go ?=>
  reset_store,
  run_model(10_000,$model,[show_probs_trunc,mean,variance,stdev
                          ]),
  nl,
  % show_store_lengths,nl,
  % fail,
  nl.
go => true.
  
  
model() =>
  DuckHunters = 5,
  Ducks = 10,

  Shoots = random_integer1_n(Ducks,DuckHunters),
  NumKilled = Shoots.remove_dups.len,
  
  add("num killed",NumKilled).