wu :: forums
« wu :: forums - Random Quadratic Equation »

Welcome, Guest. Please Login or Register.
Mar 29th, 2024, 1:37am

RIDDLES SITE WRITE MATH! Home Home Help Help Search Search Members Members Login Login Register Register
   wu :: forums
   riddles
   medium
(Moderators: Grimbal, Icarus, Eigenray, SMQ, william wu, towr, ThudnBlunder)
   Random Quadratic Equation
« Previous topic | Next topic »
Pages: 1  Reply Reply Notify of replies Notify of replies Send Topic Send Topic Print Print
   Author  Topic: Random Quadratic Equation  (Read 1300 times)
william wu
wu::riddles Administrator
*****





   
WWW

Gender: male
Posts: 1291
Random Quadratic Equation  
« on: Aug 12th, 2004, 6:18pm »
Quote Quote Modify Modify

Consider the equation Ax2 + Bx + C = 0, where A B and C are all uniformly distributed random variables over [0,1]. Compute the probability that the roots are real.
IP Logged


[ wu ] : http://wuriddles.com / http://forums.wuriddles.com
TenaliRaman
Uberpuzzler
*****



I am no special. I am only passionately curious.

   


Gender: male
Posts: 1001
Re: Random Quadratic Equation  
« Reply #1 on: Aug 13th, 2004, 12:18am »
Quote Quote Modify Modify

::
it can be easily shown that  
"If X1 and X2 are two independent rectangular variates on [0,1] then the distribution of X1X2 is -logx"
Now all that is left to find is,
P(AC<=B2/4) where B goes from 0 to 1.
This yields me ((ln2)/6)+(5/36)
::
IP Logged

Self discovery comes when a man measures himself against an obstacle - Antoine de Saint Exupery
william wu
wu::riddles Administrator
*****





   
WWW

Gender: male
Posts: 1291
Re: Random Quadratic Equation  
« Reply #2 on: Aug 13th, 2004, 9:07pm »
Quote Quote Modify Modify

That was speedy  Shocked
IP Logged


[ wu ] : http://wuriddles.com / http://forums.wuriddles.com
TenaliRaman
Uberpuzzler
*****



I am no special. I am only passionately curious.

   


Gender: male
Posts: 1001
Re: Random Quadratic Equation  
« Reply #3 on: Aug 14th, 2004, 11:29am »
Quote Quote Modify Modify

I was going through my probability notes for an examination and this question turned out to be a good exercise.  Smiley
IP Logged

Self discovery comes when a man measures himself against an obstacle - Antoine de Saint Exupery
Pages: 1  Reply Reply Notify of replies Notify of replies Send Topic Send Topic Print Print

« Previous topic | Next topic »

Powered by YaBB 1 Gold - SP 1.4!
Forum software copyright © 2000-2004 Yet another Bulletin Board