Question

The maximum time to complete a task in a project is 1 month. Suppose that the completion time as a proportion of this maximum is a beta random variable with alpha-0,5 and beta -1. A) What is the probability that the task requires more than 0,5months to complete. B) Calculate the Variance of this random variable?

Answer 1

We have, the maximum time to complete a task in a project is 1 month & the completion time as a proportion of this maximum is beta random variable.

Maximum time 1, hence it is a beta first kind distribution

i.e t ~ beta (a=0.5, b=1)

A)P(t>0.5)=0.2928932 ( by using R software )

B) variance of t

$Var\left ( t\right )= \frac{ab}{\left ( a+b \right )^{2}\left ( a+b+1 \right )}$

Variance =0.08888

R code is given below