Re: Simulation for probability of the roots of a quadratic equation
- To: mathgroup at smc.vnet.net
- Subject: [mg93108] Re: Simulation for probability of the roots of a quadratic equation
- From: Mark Fisher <particlefilter at gmail.com>
- Date: Sun, 26 Oct 2008 01:30:13 -0500 (EST)
- References: <gdrqbk$mpc$1@smc.vnet.net>
On Oct 24, 2:35 am, amzoti <amz... at gmail.com> wrote: > Hi All, > > I saw this recent thread on sci.math. > > <http://groups.google.com/group/sci.math/browse_thread/thread/ > 23ceb5aa5d883cbe/24d7ac4ba82b532f#24d7ac4ba82b532f> > > How can one do that simple simulation in Mathematica? > > Also, here is an analysis if what the probabililty should be. Do the > results above match this? > > <http://www.whim.org/nebula/math/probposdisc.html> > > Thanks ~A Mathematica knows the analytic answer as well. boole = Integrate[ Boole[b^2 - 4 a*c > 0], {a, -n, n}, {b, -n, n}, {c, -n, n}, Assumptions -> n > 0]; vol = Integrate[1, {a, -n, n}, {b, -n, n}, {c, -n, n}, Assumptions -> n > 0]; frac = Simplify[boole/vol] Compare with the simulation: ranfun = Compile[{n}, Module[{a, b, c}, Plus @@ Table[ {a, b, c} = RandomReal[{-1, 1}, 3]; If[b^2 - 4 a*c > 0, 1, 0], {n}]/n]]; Log[ranfun[10^6]/frac] --Mark