 My Math Forum Understanding the setup for the probability that $Ax^2+Bx+C$
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 March 1st, 2014, 08:41 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, 12:40 PM #2 Global Moderator   Joined: May 2007 Posts: 6,820 Thanks: 722 Re: Understanding the setup for the probability that $Ax^2+B Something is wrong with your tex. Tags$ax2, probability, setup, understanding Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post Rfeynman16 Algebra 1 January 31st, 2014 12:37 PM Rfeynman16 Algebra 3 January 2nd, 2014 12:53 PM fobbz Probability and Statistics 3 March 7th, 2013 12:45 PM supernerd707 Probability and Statistics 1 July 9th, 2012 12:52 PM bkspalding Advanced Statistics 1 October 26th, 2008 12:12 AM

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