questiona the following probability distributions

Question

Question:

a. The following probability distributions relate to the completion times, in weeks, T_A and T_B of two independent activities, A and B respectively.

t	Pr(TA =t)
2	0.20
4	0.35
6	0.25
8	0.20

t	Pr(TB =t)
3	0.25
5	0.50
7	0.25

The activities A and B form a important phase of a project.

i). Derive the probability distribution of the completion times of this phase if the two activities are undertaken in:

   a. series

   b. parallel

ii) For each of the distribution in (i) above, calculate their relevant statistics.

A task is known to have the following time to completion (in days), T and cost, C probability distribution, respectively: T ≈ N(20,25)

The distribution of C is conditional on T and is given by:

                                                              N(1500,4900),    T ≤ 22;

                                                C   ≈      N(1800,4900),    22<T ≤ 25;

                                                              N(2300,4900),    25< T.

Calculate:

i). Pr(T≤ 25);

ii Pr(C≤ 2200).