Suppose that a fire can occur at any one of five points along a road. These points are located at 3, 1, 0, 1, and

Suppose that a fire can occur at any one of five points along a road. These points are located at ˆ’3, ˆ’1, 0, 1, and 2 in Fig. 4.9. Suppose also that the probability that each of these points will be the location of the next fire that occurs along the road is as specified in Fig.

Figure 4.9 Probabilities for Exercise 9.
a. At what point along the road should a fire engine wait in order to minimize the expected value of the square of the distance that it must travel to the next fire?
b. Where should the fire engine wait to minimize the expected value of the distance that it must travel to the next fire?

0.4 0.2 0.2 0.1 0.1 Road