Eine Kugel bewege sich pro Sekunde einmal in eine der vier Richtungen [br]vor, zurück, rechts, links. Wie groß ist die Wahrscheinlichkeit, dass sie[br]sich nach 10 Sekunden noch immer in einem 5x5 großen Quadrat um den [br]Startpunkt aufhält? [br][br][br]Erzeuge Zufallszahlen 1,2,3,4 und weise den Zahlenwerten jeweils eine [br]Richtung zu. Im KO Zentrum lasse ich aus der Höhe z=10 eine Kugel fallen[br]und wo sie aufschlägt errichte ich ein Säulen-Segment und zähle die [br]Einschläge über die Segmenthöhe. [br][br]Eine Auszählung der 4^10 möglichen Züge[br][br]572544 [br]0,546020508 IN[br]0,453979492 OUT[br]476032[br][br]Full Tableau über Binomialverteilung (ohne Lücken) von rechts oben nach links unten[br][i]Sequence(Sequence(BinomialDist(A4, 1/2, i, false) BinomialDist(A4, 1/2, j, false), i, 0, A4), j, 0, A4) A2^A4[/i][br][math]\small \left(\begin{array}{rrrrrrrrrrr}1&10&45&120&210&252&210&120&45&10&1\\10&100&450&1200&2100&2520&2100&1200&450&100&10\\45&450&2025&5400&9450&11340&9450&5400&2025&450&45\\120&1200&5400&14400&25200&\textcolor{red}{30240}&25200&14400&5400&1200&120\\210&2100&9450&25200&\textcolor{red}{44100}&\textcolor{red}{52920}&\textcolor{red}{44100}&25200&9450&2100&210\\252&2520&11340&\textcolor{red}{30240}&\textcolor{red}{52920}&\textcolor{red}{63504}&\textcolor{red}{52920}&\textcolor{red}{30240}&11340&2520&252\\210&2100&9450&25200&\textcolor{red}{44100}&\textcolor{red}{52920}&\textcolor{red}{44100}&25200&9450&2100&210\\120&1200&5400&14400&25200&\textcolor{red}{30240}&25200&14400&5400&1200&120\\45&450&2025&5400&9450&11340&9450&5400&2025&450&45\\10&100&450&1200&2100&2520&2100&1200&450&100&10\\1&10&45&120&210&252&210&120&45&10&1\\\end{array}\right)[/math]
Alle Wege und Zähler eingetragen
Rekursion über 8 Richtungen 8^10 [br]↑↓ →← ↗↙↖↘[br](quasi aus versehen hab ich eine Rekursionsformel.js getestet):[br][br]k=8[br]n=10[br][br]8^10 = 1073741824[br]In: 430710168 (0.401), Out 643031656[br][br][math]\small \left(\begin{array}{rrrrrrrrrrr}1&10&55&210&615&1452&2850&4740&6765&8350&8953\\10&90&460&1650&4590&10380&19680&31860&44610&54430&58140\\55&460&2260&7860&21405&47640&89340&143520&199995&243340&259720\\210&1650&7860&26610&71070&155580&288120&458220&634170&768270&818940\\615&4590&21405&71070&187515&406320&747480&1182600&1631775&1972830&2102085\\1452&10380&47640&155580&406320&872052&1593840&2507340&3447660&4157760&4427904\\2850&19680&89340&288120&747480&1593840&2902320&4550400&6246810&7522920&8011080\\4740&31860&143520&458220&1182600&2507340&4550400&7110180&9743580&11715480&12474000\\6765&44610&199995&634170&1631775&3447660&6246810&9743580&13344030&16032240&17071740\\8350&54430&243340&768270&1972830&4157760&7522920&11715480&16032240&19246920&20494320\\8953&58140&259720&818940&2102085&4427904&8011080&12474000&17071740&20494320&21824208\\\end{array}\right)[/math][br]der 1. Quadrant des Tableaus - wird über die letzte Zeile/Spalte gespiegelt[br][br][br][size=85][i]function w8(n, x, y) {[br] if (n > 0) {[br] return w8(n - 1, x - 1, y) + w8(n - 1, x + 1, y) + w8(n - 1, x, y + 1) + w8(n - 1, x, y - 1) + [br] w8(n - 1, x - 1, y - 1) + w8(n - 1, x + 1, y + 1) + w8(n - 1, x + 1, y - 1) + w8(n - 1, x - 1, y + 1);[br] } else {[br] T[N + x][N + y] += 1[br] return 0;[br] };[br]}[br][/i][/size][br][img]data:image/png;base64,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[/img][br]