Question

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 1

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