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        riddles >> medium >> Random Quadratic Equation
        
(Message started by: william wu on Aug 12^th, 2004, 6:18pm)

Title: Random Quadratic Equation
Post by william wu on Aug 12^th, 2004, 6:18pm

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.

Title: Re: Random Quadratic Equation
Post by TenaliRaman on Aug 13^th, 2004, 12:18am

::[hide]
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)
[/hide]::

Title: Re: Random Quadratic Equation
Post by william wu on Aug 13^th, 2004, 9:07pm

That was speedy :o

Title: Re: Random Quadratic Equation
Post by TenaliRaman on Aug 14^th, 2004, 11:29am

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