Question

Maximum time to complete a task in a project is 2.5 days. suppose that the completion time as a proportion of this maximum is a beta random variable with α = 2 and β = 3. what is the probability that the task requires more than two days to complete

Answer 1

The beta distribution takes a value between 0 and 1.

The proportion of 2 days relative to max of 2.5 days is 2/2.5 = 0.8.

You want the P(x>0.8) for the beta distribution.

$= \int_{0.8}^1 \frac{ ( \alpha + \beta -1)!}{(\alpha -1)! (\beta-1)!} x^{\alpha -1} (1-x)^{\beta-1} \\ \\ = 12 \int_{0.8}^1 x(1-x)^2 \\ \\ = 0.0272$

Answer: The probability it takes more than 2 days is 2.72%