Each of x and y is a real number chosen randomly from the interval (0,1). 
z is a random variable defined as  z = x3*y

1) Find the probability that z  is in the interval (.16,.20)
2) Find the probability that z is any decimal whose first digit 
when written in scientific notation is a 1.

Bonus: Find the full probability distribution of the first digit of z.

Note: Provide all answers as exact numbers in closed form.