Suppose X and Y are independent and exponentially distributed both with unit-mean. Consider the roots of the quadratic equation ![](https://test.transtutors.com/qimg/ef723620-19b5-4562-8195-bbc0f29232b6.png)
(a) Find the probability that the roots are real.
(b) Find the probability that the roots are complex.
(c) Find the probability that the roots are equal.