Let B, C be two numbers chosen uniformly at random from [-1, 1] which are independent 1. What are density functions fB (b) and fc(c)? 2. What is f(B,C) (b, c), the joint density of B and C?

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Problem 6
Let B, C' be two numbers chosen uniformly at random from [-1, 1] which are independent.
1. What are density functions fB (b) and fc(c)?
2. What is f(B,C) (b, c), the joint density of B and C?
3. What is the probability that x² + Bx+C =0 has two different real roots?
(Hint: recall the quadratic formula, which says the roots of the above equation are
2
Transcribed Image Text:Problem 6 Let B, C' be two numbers chosen uniformly at random from [-1, 1] which are independent. 1. What are density functions fB (b) and fc(c)? 2. What is f(B,C) (b, c), the joint density of B and C? 3. What is the probability that x² + Bx+C =0 has two different real roots? (Hint: recall the quadratic formula, which says the roots of the above equation are 2
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