Please help me with these two questions

51387 Assignment
Q.2.1
Starting salary is Z
Utility is
Given that scores have a pdf as
Z’100 144 196
P 1/3 1/3 1/3
E(Starting salary) = E(z’) = (100+144+196)/3 = 146.67
Expected Utility of starting salary = E(10=10E() = 121.11
Utility of Starting salary let it be Y
Y 100 120 140
P 1/3 1/3 1/3
E(Y) = (100+120+140)/3 = 120
This is different because expectation of linear functions only obey E(aX) =aE(X)
But here square root of Z is used so these two are slightly different.
2.2
If we do not want to take the exam then you expected starting salary is 146.67
If you take the exam and suppose you score more than 146.67 your expected salary would be definitely more than this.
Hence you can go through the syllabus and find out whether you would be comfortable to get more than 146.67 score. In case you are confident, you can opt for writing final...