sydelcid/jsim

simulations in J

jsim

This directory contains some simulations done in J, an array programming language, which is very suitable to do math and puzzles very quickly, after getting used to the language!

Current list of questions

simulations.ijs

1. https://math.stackexchange.com/questions/779585/expected-number-of-spins
2. https://math.stackexchange.com/questions/2763/what-is-the-expected-number-of-runs-of-same-color-in-a-standard-deck-of-cards
3. https://math.stackexchange.com/questions/644342/probability-of-two-tens-in-a-random-shuffled-deck-of-cards
4. https://math.stackexchange.com/questions/743154/combining-random-cards-from-two-decks-and-calculating-probability
5. https://math.stackexchange.com/questions/706024/2-player-dice-game-probability
6. https://math.stackexchange.com/questions/743602/how-many-random-cards-picks-with-replacement-are-required
7. https://math.stackexchange.com/questions/798475/spinners-from-yesteryear-a-challenging-probability-problem
8. https://math.stackexchange.com/questions/795955/probability-question-with-coins
9. https://math.stackexchange.com/questions/798412/expected-value-of-a-sum-of-a-10-sided-die
10. https://math.stackexchange.com/questions/800406/broken-trucks-at-a-road
11. https://math.stackexchange.com/questions/801470/extracting-balls-from-a-basket-until-all-have-the-same-colour
12. https://math.stackexchange.com/questions/749336/k-items-in-n-buckets-number-of-buckets-with-at-least-2-items
13. https://math.stackexchange.com/questions/811516/probability-that-yz-1-xz-2
14. Probability that sum of num^6 < 1, 10 numbers taken from uniform distribution
15. https://math.stackexchange.com/questions/816803/probability-of-lies-a-point-in-a-random-triangle
16. https://math.stackexchange.com/questions/822420/probability-coin-flip

simulations-2.ijs

17. https://math.stackexchange.com/questions/66077/how-to-find-the-expected-number-of-boxes-with-no-balls
18. https://math.stackexchange.com/questions/818829/probability-in-cards-that-4-people-each-get-queen-and-king/
19. https://math.stackexchange.com/questions/823397/expected-value-and-dice
20. https://math.stackexchange.com/questions/380004/i-roll-6-sided-dice-until-the-sum-exceeds-50-what-is-the-expected-value-of-the
21. https://math.stackexchange.com/questions/733942/help-with-the-probabilty-of-rolling-two-ten-sided-dice-multiple-times-until-100
22. https://math.stackexchange.com/questions/324387/two-dice-roll-questions-related-to-rolling-a-yahtzee
23. https://math.stackexchange.com/questions/684426/on-average-how-many-times-does-one-need-to-roll-three-fair-dice-to-get-a-sum-of
24. https://math.stackexchange.com/questions/192177/how-many-times-to-roll-a-die-before-getting-two-consecutive-sixes
25. If the above question is changed to getting a '5 6' instead
26. https://math.stackexchange.com/questions/28905/expected-time-to-roll-all-1-through-6-on-a-die
27. The expected number of throws till all 6 consecutive throws show up different faces
28. https://math.stackexchange.com/questions/736211/how-many-times-does-a-single-fair-die-have-to-be-rolled-for-a-number-to-repeat
29. https://math.stackexchange.com/questions/369582/rolling-a-fair-die-4-times-what-is-the-probability-of-getting-an-increasing-seq
30. https://math.stackexchange.com/questions/339484/three-equal-die-rolls-in-a-row-in-a-3-times-3-array
31. https://math.stackexchange.com/questions/740336/the-probability-of-the-first-roll-having-the-highest-number-in-n-consecutive-rol

simulations-3.ijs

32. https://math.stackexchange.com/questions/827938/calculate-the-probability-that-at-least-k-of-his-favourite-students-are-awarded
33. https://math.stackexchange.com/questions/833911/probability-of-an-event-indicator-black-and-white-balls
34. https://math.stackexchange.com/questions/835458/expected-value-of-two-successive-heads-or-tails-stuck-on-computation
35. https://math.stackexchange.com/questions/68541/probability-question-about-married-couples
36. https://math.stackexchange.com/questions/25568/expected-number-of-rolling-a-pair-of-dice-to-generate-all-possible-sums
37. https://math.stackexchange.com/questions/838659/football-game-penalty-kicks-maximizing-winning-chances
38. https://math.stackexchange.com/questions/656310/8-cards-are-drawn-from-a-deck-of-cards-without-replacement
39. https://math.stackexchange.com/questions/842178/probability-of-modal-value-being-mode-when-rolling-dice
40. https://math.stackexchange.com/questions/846442/generating-function-probability-regaridng-coin-toss/
41. https://math.stackexchange.com/questions/846315/using-markov-chain-to-find-average-and-probability/
42. https://math.stackexchange.com/questions/847763/drawing-previously-undrawn-cards-from-a-deck/
43. https://math.stackexchange.com/questions/849751/non-geometric-way-to-calculate-expected-value-of-breaks

simulations-4.ijs

44. https://math.stackexchange.com/questions/850244/asymptoticly-how-many-random-students-do-i-have-to-mark-before-ive-marked-two
45. https://math.stackexchange.com/questions/850857/an-archery-game
46. https://math.stackexchange.com/questions/854612/the-probability-that-x-birthdays-lie-within-n-days-of-each-other
47. https://math.stackexchange.com/questions/861856/expected-number-of-parallel-tosses-where-each-coin-gets-heads-at-least-once-of
48. https://math.stackexchange.com/questions/911571/probability-rolling-a-dice-5-times
49. https://math.stackexchange.com/questions/953908/probability-that-the-sum-of-three-integer-numbers-from-1-to-100-is-more-than-1
50. https://math.stackexchange.com/questions/951236/probability-of-exactly-2-low-rolls-in-5-throws-of-a-die
51. https://math.stackexchange.com/questions/1061083/average-time-to-fill-boxes-with-balls/
52. https://math.stackexchange.com/questions/1097630/break-a-stick-into-2-expected-length-of-shorter-stick
53. https://math.stackexchange.com/questions/1157960/basic-card-dealing-probability
54. https://math.stackexchange.com/questions/1325895/direction-on-how-to-rightly-compute-a-certain-expected-value
55. https://math.stackexchange.com/questions/1334544/off-by-1-lottery-probability

simulations-5.ijs

56. https://math.stackexchange.com/questions/1485546/how-many-tickets-should-i-buy-to-win-a-prize-in-lottery
57. Seven boys and three girls are seated in a row. Find the number of ways of seating arrangements such that the boys get the end positions and no two girls are seated next to each other.
58. https://math.stackexchange.com/questions/2094936/expected-length-of-a-sequence
59. https://puzzling.stackexchange.com/questions/57583/how-many-tries-to-roll-a-6