3. Correct. The answer is false. In order to calculate the value of 'a', we have to calculate the definite integral of the density function between 0 and 1. Remember that the the value of the integral of density function over its domain is equal to 1.
1 = a [1/2 - 1/3] => a = 6
The graph of this 'oil discovery function' (a probabilistic density function) is: