Given the following model

$y_i=$widehat$({)}_0+$widehat$({)}_1{x}_1+{}_i$

a$.$ Find the Variance of widehat$({)}_0.$

b$.$ Prove that $\frac{?}{\text{b}\text{a}\text{r}}({)}_0$ is unbiased.

Question $2-20$ Marks

The University Hospital of the West Indies found itself the subject of several unflattering articles about it's botched implementation of an electronic health records management system $($EHRMS$).$ As a result, Minister Tufton has asked you to conduct and complete a formal investigation within $2$ weeks.

a$)$ In your interview with the Project Manager, he explained that the first phase of execution was to transform the Billings process which was largely manual at the time. The requirements documentation included a map of the current process as well as the desired process. However, halfway through implementation of the Billings software module, several departments changed when and how they supplied to the Accounts department information essential to the Billing process. This was done without any consultation with the Project Team. Since then some persons have loudly suggested that an agile approach would have prevented this problem.

Define and differentiate among the following development approaches:

Predictive

Iterative

Incremental

Hybrid

Agile

$(10$ Marks$)$

b$)$ Now that you are aware of the potential for changes mid$-$stream, suggest how you would reduce this risk to the implementation of the EHRMS. $(5$ marks$)$

c$)$ More than half of the implementation cost is paid to a contracted software development and project management firm. Write a memo for the procurement team explaining how five different contract types can shift risk between the UHWI and its contractors.

$(5$ Marks$)$