bpv.sh

#!/bin/bash

display_usage() {
	echo -e "Usage:\n\t$0 <p> <n> <x>\n"
}

if [  $# -le 2 ]; then
	display_usage
	exit 1
fi

bc << EOF
define ncx(n, x)
{
    auto a, b, i

    a = 1
	for(i = (x + 1); i <= n; i++)
	{
	  a *= i;
	}

    b = 1
	for(i = 1; i <= (n - x); i++)
	{
	  b *= i;
	}

    return a / b
}

define binprob(p, n, x)
{
    auto v

    v = ncx(n, x)
    v *= (1 - p) ^ (n - x)
    v *= p ^ x

    return v
}

define r(x, d)
{
    auto r, s

    if(0 > x) {
        return -r(-x, d)
    }
    r = x + 0.5*10^-d
    s = scale
    scale = d
    r = r*10/10
    scale = s
    return r
}

calcscale = 30
outscale = 4

x = $3
n = $2
p = $1
x0 = x
x1 = $4

if (x1 < x)
{
  x1 = x
}

s = 0
while (x <= x1) {

	scale = calcscale
	v = r(binprob(p, n, x), outscale)
	s += v

	scale = outscale
	print "p = ", p/1, "\n"
	print "n = ", n, "\n"
	print "P(X = ", x, ") = ", v/1 , "\n"

	x = x + 1
}

print "SUM (X = ", x0, "..", x1, ") = ", s/1 , "\n"

EOF