1.
Your regular tennis partner has offered a friendly wager to you. The two of you will play out one point in which you can serve. The loser pays the winner $100. If your first serve is not in play, you get a second serve. If your second serve is not in play, you lose the point.
You have two kinds of serves: a hard one and a soft one. You know that your hard serve is in play 65% of the time and, when it is in play, you win the point 75% of the time. You put your soft serve in play 88% of the time and, when it is in play, you win the point 27% of the time.
Construct a Decision Tree for this problem and answer the following questions:
Should you accept the wager?
What is the Expected Monetary Value?
If so, should you use your hard or soft serve?
2.
A graduate student has variable income from his assistanceship and tutoring work. He extimates his monthly income (as of the beginning of the month) to follow follow this distribution:
Income
Probability
$850
0.35
$900
0.25
$950
0.25
$1,000
0.15
His monthly expenses are expected to range from $850 to $1,200, following a uniform distribution.
He has a beginning cash balance in September of $1,500.
1. What is his expected cash balance at the end of the following May?
2. What is the probability that his balance will be negative in one or more month?
3. What is the probability that his May ending balance is less than $500?
3.
Fred’s Fasteners is a manufacturing company that has decided they are large enough to choose to be self-insuring for employee health insurance. The Chief Financial Officer has asked for some projections on the costs to the company for the next fiscal (also a calendar) year. Analysts studying records for prior periods have decided on the following assumptions.
January employment level will be 9,250, and is expected to increase in subsequent months by a percentage randomly chosen from a uniform distribution, minimum of -2%, maximum of 4%
Each emplyee will contribute $325 per month….