Question

In: Statistics and Probability

Let A, B, and C be independent random variables, uniformly distributed over [0,4], [0,2], and [0,3]...

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?

Solutions

Expert Solution

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

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

orchestra answered 1 year ago

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