Two quantities, $a$ and $b$, are estimated as the minimum and maximum length of time it will take for a project to be completed. Experience shows that the actual length of time it takes for a project to be completed is a random variable defined by $Y = a + (b-a)X$, where $X\sim \mathrm{Beta}(\alpha,\beta)$, where $\alpha$ and $\beta$ are also determined for each project. Suppose that for a particular project it is estimated $a=2$ years, $b=4$ years, $\alpha = 2$ and $\beta = 2$.
How do I find the mean and variance of the time it will take to complete the project?
What is the probability it will take less than 3 years to complete the project?