//-------------------------------------------------------------------
//	normdist.cpp
//
//	This program displays a probability distribution and graph
//	for the Normal Distribution having parameters  n  and  p .
//
//		to compile:  $ g++ normdist.cpp -o normdist
//		to execute:  $ ./normdist
//
//	programmer: ALLAN CRUSE
//	written on: 21 FEB 2011
//-------------------------------------------------------------------

#include <stdio.h>	// for printf()  
#include <math.h>	// for sqrt(), exp()

#define N_MAX	50

double	p = 0.50;	
double	mu, sigma;

double freq( double x )
{
	// returns the value of the normal distribution at x
	double	pi = 3.1415926589793;
	double	sqroot_2pi = sqrt( 2.0 * pi );
	double	den = (sqroot_2pi * sigma);
	double	arg = ( x - mu ) / sigma;
	double	num = exp( - arg*arg / 2.0 );
	return	num / den;	
}

int main( int argc, char **argv )
{
	// initialize global variables
	int	n = N_MAX;
	mu = n * p;
	sigma = sqrt( mu * (1.0 - p) );

	// exhibit the normal distribution function
	printf( "\n" );
	printf( " Normal probability distribution" );
	printf( " for n=%d and p=%1.5f \n\n", n, p );
	for (int k = 0; k <= n; k++)
		{
		double	prob = freq( (double)k );
		printf( " k=%-3d ", k );
		printf( "prob=%1.5f ", prob );
		int	m = (int)( 300.0 * prob );
		for (int j = 0; j < m; j++) printf( "*" );
		printf( "\n" );
		}

	// report this distribution's statistical parameters
	printf( "\n n=%d  mu=%1.5f  sigma=%1.5f \n\n", n, mu, sigma );
}