In: Statistics and Probability
Let A, B, and C be independent random variables, uniformly distributed over [0,4], [0,2], and [0,3] respectively. What is the probability that both roots of the equation Ax2+Bx+C=0 are real?
From given data,
Let A, B, and C be independent random variables, uniformly distributed over [0,4], [0,2], and [0,3] respectively.
Ax2+Bx+C=0
For real solution
B2 - 4 AC > 0
B2 > 4 AC
Since
A = [0,4]
B = [0,2]
C = [0,3]
B2 > 4 AC
so we can square root both side
B> 2
Also , maximum value of 2
= 2
= 2
Which is less than maximum value of B = 2
Limits
0 < A < 4
0 < C < 3
2 < B < 2
Volume over which we are integrating:
4*3*2 = 24
So you must divide by 24
= 1/24* (-12.95042)
P = -0.5396