Six risk scenarios, from a binomial loan pool to correlated defaults, each solved with its rule named and its result read as money or odds: GF582's Unit 3 probability problem set. Searches like "gf 582 unit 3 assignment example", "gf582 unit 3 sample" and "gf582 unit 3 example" land here.
What a finished GF582 Unit 3 probability problem set looks like
Six problems over about five pages, each in four parts: the setting, the distribution or rule and why it fits, the working with an Excel function shown, and a closing line reading the result for the lender or investor. Problem one finds a 36.3 percent chance that a pool of 40 loans, each with a 2.5 percent default probability, sees no default at all, and a 7.8 percent chance of three or more. Problem two applies Bayes' rule to a flag catching 70 percent of defaulters and 8 percent of good borrowers, so a flagged account defaults only 21.3 percent of the time. Problem three prices expected loss at 2,025 dollars on one loan. Problems four to six cover a normal return distribution, Poisson fraud chargebacks and correlated defaults.
How a GF582 Unit 3 example is structured
Problems are ordered by the assumption each one leans on, so that the last can break the assumption the first needed. Problem one assumes independence and says so, since the binomial result depends on it. Problem two turns on a base rate: with only 3 percent of borrowers defaulting, most flags land on good accounts, which the sample reads as a staffing question, not a flaw in the flag. Problem three combines probability with exposure and severity. Problem four puts a 6.7 percent chance on a loss worse than 10 percent in a year from a 6.5 percent mean and 11 percent deviation, then warns that real returns have fatter tails. Problem five finds a 4.5 percent chance of seven or more chargebacks in a day. Problem six restores dependence: at a correlation of 0.30, joint default is 6.7 times the independent figure.
A pool assumed independent
BINOM.DIST with 40 trials and 2.5 percent gives 0.3632 for zero defaults and 0.0779 for three or more. The problem states that loans to firms in one town or one trade rarely fail independently.
A flag and its base rate
Of flagged accounts, 21.3 percent default: 0.021 out of a total flag rate of 0.0986. The answer reads as roughly four false alarms for each true one, which sets how much review time a flag deserves.
Expected loss on one loan
Exposure of 180,000 dollars, a 2.5 percent default probability and 45 percent severity give 2,025 dollars. The sentence after it notes that expected loss is an average and no single loan loses that amount.
Chargebacks counted as Poisson
At an average of 3.2 a business day, the chance of seven or more is 4.46 percent, about eleven days in a 250-day year. The problem checks that events arrive singly and independently before using the model.
Linked failures
Two loans at 5 percent each fail together 0.25 percent of the time if independent and 1.675 percent at a default correlation of 0.30. The set closes on why diversification tables built on independence understate joint losses.
Where marks go in GF582 Unit 3
Probability sets in GF582 lose the most when the distribution is chosen by habit, a normal curve applied to a count of defaults or a binomial applied to events with no fixed number of trials. Most sections require the choice justified in a sentence, and an answer arriving with no stated conditions forfeits part of the method credit however accurate the figure. Base-rate problems are where the conceptual loss concentrates: reading a flag's 70 percent catch rate as a 70 percent chance that a flagged borrower defaults. Results left as decimals with no business sentence miss the interpretation marks. Independence assumed silently in a lending pool, and never questioned, is a further deduction in sections that teach correlation. Excel functions shown without their arguments make the work hard to check.
Get a GF582 Unit 3 example written to your instructions
The Unit 3 set as your instructor issued it, scenarios, rates and any Excel requirements, plus the rubric: that is the whole input. Each problem in the custom solution names its distribution, shows the working and ends on a sentence of business meaning, back within 24-48h and free the first time.
GF582 Unit 3 questions, answered
How do I know which distribution a problem calls for?
Read what is being counted or measured. A fixed number of independent yes-or-no trials suggests the binomial; events arriving at an average rate over time suggest the Poisson; a continuous quantity such as a return suggests a continuous distribution, often the normal as a first approximation. Write the conditions down, then check the problem actually meets them before calculating.
Why does a flag that catches most defaulters still produce mostly false alarms?
Because defaulters are rare. When only 3 percent of borrowers default, even a small false-alarm rate applied to the other 97 percent produces more wrong flags than right ones. Bayes' rule makes this precise. The finding is not that the flag is useless, but that its value depends on what a flag triggers and what that response costs.
Is it acceptable to use Excel functions instead of formulas?
In most sections, yes, provided the function and its arguments are shown so a reader can check them. BINOM.DIST, POISSON.DIST and NORM.DIST cover most of this unit. Writing the formula once beside the function, even briefly, shows you understand what the software computed, which is often what the method criterion rewards.