- #1
stepheckert
- 6
- 0
I am trying to solve for probabilities in systems with a large number of elements. To deal with the large factorials that appear in these formulas, I use Stirling's formula, lnm!=mlnm-m+(1/2)ln(2πm). My problem is that after I get the approximation and try to plug it into the probability formula, N!/(n!(N-n)!)(p^n)(q^(N-n)), I get overflows on my calculator. How can I get around this?
Here is an example problem:
Using Stirling's formula, calculate the probability of getting exactly 500 heads and 500 tails when flipping 1000 coins.
The probability equation looks like: (1000!/(2!998!))(1/2)^2(1/2)^998
I used lnm!=mlnm-m+(1/2)ln(2πm) to get: ln998!=5898.3 and ln1000!=5912.2
I wound up with somehting that looked like this: (e^5912.2/2e^5898.3)(1/2)^2(1/2)^998
How do I get my calculate to work with these kind of numbers??
Thanks for any help!
Here is an example problem:
Using Stirling's formula, calculate the probability of getting exactly 500 heads and 500 tails when flipping 1000 coins.
The probability equation looks like: (1000!/(2!998!))(1/2)^2(1/2)^998
I used lnm!=mlnm-m+(1/2)ln(2πm) to get: ln998!=5898.3 and ln1000!=5912.2
I wound up with somehting that looked like this: (e^5912.2/2e^5898.3)(1/2)^2(1/2)^998
How do I get my calculate to work with these kind of numbers??
Thanks for any help!