You know that in one year you are going to buy a house. (In fact, you have already selected the neighborhood, but right now you are finishing your graduate degree and you are engaged to be married this summer, so you are delaying the purchase for a year.) The annual interest rate for fixed-rate 30-year mortgages is currently 6.00%, and the price of the type of house you are considering is $120,000. However, things may change. Using your knowledge of the economy (and a crystal ball), you estimate that the interest rate might increase or decrease by as much as one percentage point. Also, the price of the house might increase by as much as $10,000-it certainly won't decrease. You assess the probability distribution of the interest rate change as shown below.
Interest Rate Change
| Change in annual rate |
Probability |
| Down 1.0% |
0.02 |
| Down 0.75% |
0.03 |
| Down 0.5% |
0.05 |
| Down 0.25% |
0.10 |
| No change |
0.40 |
| Up 0.25% |
0.20 |
| Up 0.5% |
0.10 |
| Up 0.75% |
0.07 |
| Up 1.0% |
0.03 |
Price increase
| Increase in house price |
Probability |
| No increase |
0.2 |
| Up $5000 |
0.5 |
| Up $10,000 |
0.3 |
The probability distribution of the increase in the price of the house is also shown in this file. Finally, you assume that the two random events (change in interest rate, change in house price) are probabilistically independent. This means that the probability of any joint event, such as an interest increase of 0.50% and a price increase of $5000, is the product of the individual probabilities.
Albright, S. Christian; Winston, Wayne; Zappe, Christopher (2010-10-12). Data Analysis and Decision Making (Page 192). Cengage Textbook. Kindle Edition.