I need computer code written for the following : Please ask me if you need any o

Question

I need computer code written for the following : Please ask me if you need any other information, I need this ASAP and will give maximum points for any help.

Consider a random walk problem in one dimension.

a) If N = 10, calculate (1 ) 1 for 61 < 8.

b) If N = 300, calculate (1 ) 1 for 180 1 < 240.

c) By using the Gaussian (normal) distribution, calculate () for each case. Compare the results with those of parts a) and b).

Please round to four significant figures. please State what computer system notation you are using for example Linux, python.

here is a screen shot of the problem :

Explanation / Answer

1.

Using the Euler's theorem for Modular Multiplicative inverse.
nCr mod p can be written as   n! / (n-r)!r! mod p   
which is equal to n! * ((n-r)!*r!))^-1 mod p now let
x= ((n-r)!*r!)) . Now the problem is just to find out what the inverse of x mod p would be .
Euler's theorem states that when p is prime then x^-1 mod p = x^(p-2) mod p . This should be easy to calculate using the Modular exponentiation

2.

#include <SPFD5408_Adafruit_GFX.h> // Core graphics library #include <SPFD5408_Adafruit_TFTLCD.h> // Hardware-specific library #include <SPFD5408_TouchScreen.h> #define YP A1 // must be an analog pin, use "An" notation! #define XM A2 // must be an analog pin, use "An" notation! #define YM 7 // can be a digital pin #define XP 6 // can be a digital pin // Calibrate values #define TS_MINX 125 #define TS_MINY 85 #define TS_MAXX 965 #define TS_MAXY 905 TouchScreen ts = TouchScreen(XP, YP, XM, YM, 300); #define LCD_CS A3 #define LCD_CD A2 #define LCD_WR A1 #define LCD_RD A0 // optional #define LCD_RESET A4 // Assign human-readable names to some common 16-bit color values: #define BLACK 0x0000 #define BLUE 0x001F #define RED 0xF800 #define GREEN 0x07E0 #define CYAN 0x07FF #define MAGENTA 0xF81F #define YELLOW 0xFFE0 #define WHITE 0xFFFF #define MINPRESSURE 10 #define MAXPRESSURE 1000 Adafruit_TFTLCD tft(LCD_CS, LCD_CD, LCD_WR, LCD_RD, LCD_RESET); String Key[4][4] = { { "7", "8", "9", "/" }, { "4", "5", "6", "*" }, { "1", "2", "3", "-" }, { "C", "0", "=", "+" } }; String N1, N2, ShowSC, opt; bool updata=false; float answers=-1; void setup() { Serial.begin(9600); tft.reset(); tft.begin(0x9341); // SDFP5408 tft.setRotation(2); tft.fillScreen(BLACK); tft.fillRect(0, 80, 240, 240, WHITE); tft.drawFastHLine(0, 80, 240, BLACK); tft.drawFastHLine(0, 140, 240, BLACK); tft.drawFastHLine(0, 200, 240, BLACK); tft.drawFastHLine(0, 260, 240, BLACK); tft.drawFastHLine(0, 320-1, 240, BLACK); tft.drawFastVLine(0, 80, 240, BLACK); tft.drawFastVLine(60, 80, 240, BLACK); tft.drawFastVLine(120, 80, 240, BLACK); tft.drawFastVLine(180, 80, 240, BLACK); tft.drawFastVLine(240-1, 80, 240, BLACK); for (int y=0;y<4;y++) { for (int x=0;x<4;x++) { tft.setCursor(22 + (60*x), 100 + (60*y)); tft.setTextSize(3); tft.setTextColor(BLACK); tft.println(Key[y][x]); } } } void loop() { TSPoint p = waitTouch(); Serial.println(p.x); updata = false; for (int i1=0;i1<4;i1++) { for (int i2=0;i2<4;i2++) { if ((p.x>=240-((i1+1)*60)+1&&p.x<=240-(i1*60)-1)&&(p.y>=(i2*60)+1&&p.y<=((i2+1)*60)-1)) { if ((i1<=2&&i2<=2)||(i1==3&&i2==1)) { if (opt==0) { if (answers!=-1) answers = -1; N1 = N1 + Key[i1][i2]; ShowSC = N1; } else { N2 = N2 + Key[i1][i2]; ShowSC = opt + N2; } } else { if (Key[i1][i2]=="C") { N1 = N2 = ""; opt = ""; answers = 0; ShowSC = N1; } else if (i2==3) { if (N1=="") N1 = String(answers); opt = Key[i1][i2]; ShowSC = Key[i1][i2]; } else if (Key[i1][i2]=="=") { if (opt=="+") answers = N1.toInt() + N2.toInt(); else if (opt=="-") answers = N1.toInt() - N2.toInt(); else if (opt=="*") answers = N1.toInt() * N2.toInt(); else if (opt=="/") answers = N1.toInt() / N2.toInt(); N1 = N2 = opt = ""; ShowSC = answers; } } updata = true; } } } if (updata) { tft.fillRect(0, 0, 240, 80, BLACK); tft.setCursor(10, 10); tft.setTextSize(3); tft.setTextColor(WHITE); tft.println(ShowSC); } delay(300); } TSPoint waitTouch() { TSPoint p; do { p = ts.getPoint(); pinMode(XM, OUTPUT); pinMode(YP, OUTPUT); } while((p.z < MINPRESSURE )|| (p.z > MAXPRESSURE)); p.x = map(p.x, TS_MINX, TS_MAXX, 0, 320); p.y = map(p.y, TS_MINY, TS_MAXY, 0, 240);; return p; }

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