#$)$ An engineering faculty is planning to organize a conference on renewable energy systems. The project team has come up with the following Risk Checklist and determined the occurrence probability and monetary impacts for each risk.

RISK ITEM

Probability of

Expected Impact

Not being able to find enough number of sponsors

Not being able to reach targeted number of participants

Not being able to find a suitable conference venue

Bad weather conditions on the day of the conference

Having a similar event on the same week

Not being able to find high caliber speakers to attract participants

Occurrence

$0\mathrm{.}200$

$0\mathrm{.}300$

$0\mathrm{.}150$

$0\mathrm{.}100$

$0\mathrm{.}050$

$0\mathrm{.}200$

$($Monetary loss $-$ $$)$

$40,000$

$20,000$

$50,000$

$20,000$

$50,000$

$10,000$

Perform a risk analysis using the simulation approach employing $60$ replications. State your assumptions, if any.

a$)(10$ points$)$ State and explain your pseudorandom number generator method.

b$)(40$ points$)$ Report the mean and standard deviation of total impact.

c$)(10$ points$)$ Display through a histogram the distribution obtained for the total impact in intervals of $10\mathrm{.}000$ $$,$ i$.$e$.,010\mathrm{.}000$;$10\mathrm{.}001-20\mathrm{.}000$;dots.. State the interval representing the mode.

d$)(5$ points$)$ What is the probability that the expected total impact is $3\mathrm{.}000$$ $?$

e$)(5$ points$)$ What is the probability that the expected total impact is $64\mathrm{.}000$$$?$

f$)(30$ points$)$ A colleague of yours suggests a mitigation means costing $12\mathrm{.}000$$$,$ which will reduce the probability of occurrence of the third risk item by $50\%.$ What would be your saving in expected total impact? Would you accept this proposal?