A continuous probability distribution is given by a parabola, y=f(x), for a < x < 2b -a. The minimum of the parabola is at 0.5 = f(b).
a. Find the equation of the parabola in terms of a and b.
b. Find the probabilities:
i. P( a < x < b)
ii. P( x > 2b - a/2)