Suppose that the construction of a solar power station is initiated. The project’s completion time has not been set due to uncertainties in financial resources. The completion time for the first phase is modeled with a beta distribution and the minimum, most likely (mode), and maximum completion times for the first phase are 1.0, 1.25, and 2.0 years, respectively. Also, the mean time is assumed to equal μ = 1+ 4(1.25) + 2) / 6 = 1.333. Determine the following in parts (a) and (b):

(a) Parameters α and β of the beta distribution.

(b) Standard deviation of the distribution.

(c) Sketch the probability density function.