1. f we pick a number k randomly from the uniform distribution on [0,1], what is the probability that the equation x2 + 5kx + 1 = 0 has 2 distinct real roots? (Hint: The quadratic equation ax2 + bx + c = 0 has 2 distinct real roots if and only if b2 4ac > 0.)

2. If we pick a number k randomly from the normal distribution with = 1, = 2; what is the probability that the equation x2 + kx + 1 = 0 has 2 distinct real roots?