Binomial Probability Distribution

[Dieter]

(05-24-2015 05:58 PM)Dave Britten Wrote:  Running it with inputs 120, 1/6, 40, 120 yields 6.419629920E-6 in just over a minute. Compare to the version on my 48 using a direct summation of terms and repeated COMB calls returning 6.4196298769E-6. That's an error of 6.71E-7%, which isn't a terrible sacrifice for having the program finish inside of a lunar cycle (or possibly solar orbit) now.

The HP41 works with 10 digits, the HP48 with 12. For the former 1/6 equals 0,166 666 666 7, for the latter it's 0,166 666 666 667.

This means:

• The correct result for p=1/6 is 6,4196298765918... E–6
• The correct 10-digit result for p=0,1666666667 is 6,419629908 E–6.
  So the HP41 is pretty close.
• The correct 12-digit result for p=0,166666666667 is 6,41962987691 E–6.
  So the HP48 is very close. Since COMB is an internal function and thus most probably exact in all 12 digits, this could be expected.
• Compared to the true result with p exactly 1/6, both calculators offer similar accuracy: 8 out of 10 digits resp. 10 out of 12. ;-)
  

BTW my program returns the same result as yours. It has 70 steps including the COMB routine and the example runs in 53 seconds.

Dieter