Question

Suppose that A, B, C, are independent random variables, each being uniformly distributed over (0, 1). (a) What is the joint cumulative distribution function of A, B, C? (b) What is the probability that all of the roots of the equation Ax2 + Bx + C = 0 are real?

Answer 1

Answer:

a)  F (A , B,C)(a,b,c) = abc

b) Answer is in derivative

Step-by-step explanation:

Hence area is maximum x=6

For ( a,b,c) ∈ (0,1)

We have that      

F A, B,C (a,b,c) = A≤ a , B≤ b , C≤c

                        =P (A≤a) P (B≤b) P (C≤c)

A , B, C ≈ unit  (0,1) we have that

  P (A≤a) =a

 P (B≤b) =b

   P (C≤c)=c

Thus

F (A , B,C)(a,b,c) = abc

b) Answer is in derivative