A community center provides recreation facilities for young people. The impact on the community is lower crime rates. Assume there are two states of crime rates – low (L) and high (H). Observed crime rates over time show that if the crime rate is low in any month, the probability of having a low rate the following month is 0.5. The probability of having a high-rate month following a low-rate month is 0.5. If the rate is high in a month, the probability of a high rate the following month is 0.9, and thus the probability of a low rate is 0.1. These probabilities apply if the community center does not advertise. This is the do-nothing policy. (Policy n). These conditional probabilities are shown in Figure 1. However, if the center advertises its recreation programs, (policy a) the conditional probabilities change to those shown in Figure 2. The community center can change its policy at the beginning of each month. The high crime month costs 20 more than the low crime month, and advertising costs 10 per month. Month t+1 Month t+1 Policy n: L H Policy a: LH Month t: L 0.5 0.5 Month t: L 0.8 0.2 0.1 0.9 H 0.6 0.4 Fig 1. Fig 2.

A community center provides recreation facilities for young people. The impact on the community is lower crime rates. Assume there are two states of crime rates – low (L) and high (H). Observed crime rates over time show that if the crime rate is low in any month, the probability of having a low rate the following month is 0.5. The probability of having a high-rate month following a low-rate month is 0.5. If the rate is high in a month, the probability of a high rate the following month is 0.9, and thus the probability of a low rate is 0.1. These probabilities apply if the community center does not advertise. This is the do-nothing policy. (Policy n). These conditional probabilities are shown in Figure 1. However, if the center advertises its recreation programs, (policy a) the conditional probabilities change to those shown in Figure 2. The community center can change its policy at the beginning of each month. The high crime month costs 20 more than the low crime month, and advertising costs 10 per month. Month t+1 Month t+1 Policy n: L H Policy a: LH Month t: L 0.5 0.5 Month t: L 0.8 0.2 0.1 0.9 H 0.6 0.4 Fig 1. Fig 2.

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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