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March 1st, 2014, 09:41 PM  #1 
Newbie Joined: Mar 2014 Posts: 1 Thanks: 0  Understanding the setup for the probability that $Ax^2+Bx+C$
Suppose that $A, B,$ and $C$ are independent random variables, each being uniformly distributed over $(0,1)$. What is the probability that $Ax^2 + Bx + C$ has real roots? First, I set $P(B^2  4AC \ge 0)$ Then I am told that $$\begin{align} \int_0^1 \int_0^1 \int_{\min\{1, \sqrt{4ac}\}}^1 1 \;\text{d}b\,\text{d}c\,\text{d} &a= \int_0^1 \int_0^{\min\{1, 1/4a\}}\int_{\sqrt{4ac}}^1 1\;\text{d}b\,\text{d}c\,\text{d}a\\ &= \int_0^{1/4} \int_0^1 \int_{\sqrt{4ac}}^1 1\;\text{d}b\,\text{d}c\,\text{d}a + \int_{1/4}^1 \int_0^{1/4a}\int_{\sqrt{4ac}}^1 1\;\text{d}b\,\text{d}c\,\text{d}a \end{align}$$ why the middle integrate from 0 to min{1, 1/4a} from the second integral...where does 1/4a come from? why the min{...} does not go to the front integral? why they break up into last step like this (I refer to one integral + another integral) ? Thanks a lot 
March 2nd, 2014, 01:40 PM  #2 
Global Moderator Joined: May 2007 Posts: 6,684 Thanks: 658  Re: Understanding the setup for the probability that $Ax^2+B
Something is wrong with your tex.


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