Suppose that $\displaystyle A, B, C,$ are independent random variables, each being uniformly distributed over $\displaystyle (0,1).$

(a) What is the joint cumulative distribution function of $\displaystyle A, B, C?$

(b) What is the probability that all the roots of the equation $\displaystyle Ax^2 + BX + C = 0$ are real?