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 proportion of completion within one year has a beta distribution with parameters α =1 and β = 5. Determine the following:

(a) Mean and variance of the proportion completed within one year

(b) Probability that more than half of the project is completed within one year

(c) Proportion of the project that is completed within one year with probability 0.9