Let ?, ?, and ? be independent random variables, uniformly distributed over [0,5], [0,1], and [0,2] respectively. What is the probability that both roots of the equation ??^2+??+?=0 are real?
Answer:
Given that:
Let A, B, and C be independent random variables, uniformly distributed over [0,5], [0,15], and [0,2] respectively.
Ax2+Bx+C=0
For real solution
B2 - 4 AC > 0
B2 > 4 AC
Since
A = [ 0,5]
B = [0,1]
C = [0,2]
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 = 1
Limits
0 < A < 5
0 < C < 2
2 < B < 1
Volume over which we are integrating:
5*2*1 = 10
So you must divide by 10
Let ?, ?, and ? be independent random variables, uniformly distributed over [0,5], [0,1], and [0,2]...
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