Pessimistic time and optimistic time of completion of an activity are given as 10 days and 4 days respectively, the variance of the activity will be 

Concept:

Project Evaluation and Review Technique (PERT) is probabilistic in nature and is based upon three-time estimates to complete an activity.

Optimistic Time (to): It is the minimum time that will be taken to complete an activity if everything goes according to the plan.

Pessimistic Time (tp): It is the maximum time that will be taken to complete an activity when everything goes against the plan.

Most likely time (tm): It is the time required to complete a project when an activity is executed under normal conditions.

Average or most expected time is given by 

The variance gives the measure of uncertainty of activity completion. The variance of the activity is given by 

Variance, 

Standard duration, 

Calculation:

Given:

t_p = 10 days, t_o = 4 days

The variance of the activity is 1.