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Topic: Random Quadratic Equation (Read 1308 times) |
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william wu
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Random Quadratic Equation
« on: Aug 12th, 2004, 6:18pm » |
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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.
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TenaliRaman
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I am no special. I am only passionately curious.
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Re: Random Quadratic Equation
« Reply #1 on: Aug 13th, 2004, 12:18am » |
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:: 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) ::
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Self discovery comes when a man measures himself against an obstacle - Antoine de Saint Exupery
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TenaliRaman
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Re: Random Quadratic Equation
« Reply #3 on: Aug 14th, 2004, 11:29am » |
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I was going through my probability notes for an examination and this question turned out to be a good exercise.
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Self discovery comes when a man measures himself against an obstacle - Antoine de Saint Exupery
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