Consider a triangular distribution (probability density function) for an activity’s duration as in Figure E7.1a where, t1 is an optimistic duration, t3 is a pessimistic duration and t2 is the most likely duration. Note, there is a discontinuity at t = t2. Figure E7.1b shows the associated cumulative distribution function.

Show that the relevant transformation between the standard uniform variate V, and T is t = t2−t1 t3−t1 v1/2 +t1 0

(Hint. You may find the integration of the line equation of the first part of the probability density function for T easier if you first shift the origin of the line to t =t1, and the integration of the line equation for the second part of the probability density function for T easier if you next shift the origin to t = t3.)