/* 

  Geometric counting cars in Picat.

  From Mathematica (GeometricDistribution) 
  """
  A person is standing by a road counting cars until he sees a red one, 
  at which point he restarts the count. Simulate the counting process, assuming 
  that 20% of the cars are red:

    RandomVariate(GeometricDistribution(0.2), 20)
    -> 
     (10,0,2,0,2,10,8,4,0,0,15,4,4,1,6,1,6,1,0,0)

  Find the expected number of cars to come by before the count starts over:
    Mean(GeometricDistribution(0.2))
    -> 4

  Find the probability of counting 10 or more cars before a red one:
    NProbability(x >= 10, x -> GeometricDistribution(0.2))
    -> 
    0.107374

  """

  Picat> X=geometric_dist_n(0.2,20)
  X = [4,4,1,3,1,11,0,2,0,1,7,1,1,11,0,2,1,10,24,2]

  Exact probabilities:
  Picat> X=geometric_dist_mean(0.2)  
  X = 4.0

  Picat> X=1-geometric_dist_cdf(0.2,9) 
  X = 0.1073741824


  Cf my Gamble model gamble_geometric_counting_cars.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 : v
  Probabilities (truncated):
  0: 0.2007000000000000
  1: 0.1583000000000000
  2: 0.1271000000000000
  3: 0.0992000000000000
  .........
  44: 0.0001000000000000
  42: 0.0001000000000000
  41: 0.0001000000000000
  35: 0.0001000000000000
  mean = 4.0888

  var : p
  Probabilities:
  false: 0.8852000000000000
  true: 0.1148000000000000
  mean = [false = 0.8852,true = 0.1148]

*/
go ?=>
  reset_store,
  run_model(10_000,$model,[show_probs_trunc,mean]),
  nl,
  % show_store_lengths,nl,
  % fail,
  nl.
go => true.
  
  
model() =>
  V = geometric_dist(2/10),
  P = check(V >= 10),
  
  add("v",V),
  add("p",P).