1. (10 points) Consider the polynomial p(x) = x2 + P . x + Q, where P and Q are independent random variables with P ~ u(0, 1) and Q ~ exp(1). a What is the probability that p(x) has two real roots? b) Let the random variable R denote the minimal value which is attained by the polynomial p(x), i.e. R = min{x2 + P . x + Q : x E R}. Determine P(R