The three random variables, a, b and c are independent and each uniformly distributed in the interval (0, 1]. Find the probability that the equation ax? + bx +c = 0 has 2 real roots.
The three random variables, a, b and c are independent and each uniformly distributed in the interval (0, 1]. Find the probability that the equation ax? + bx +c = 0 has 2 real roots.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Step 1
We can find the roots of any quadratic equation using the discriminant as follows:
Let .
The distribution of y is given by
Let . Then the distribution of z is given by
Since y and z are independent, the joint pdf is given by
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