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.
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![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:
Policy a:
L.
H
Month t: L
0.5
0.5
Month t: L 0.8
0.2
H.
0.1
0.9
H 0.6
0.4
Fig 1.
Fig 2.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F85e69199-caf8-4942-800f-a6bbae2a2e68%2Fac86f40c-72e1-4793-99a3-bac7255c5079%2Fopobe8o_processed.jpeg&w=3840&q=75)
Transcribed Image Text: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:
Policy a:
L.
H
Month t: L
0.5
0.5
Month t: L 0.8
0.2
H.
0.1
0.9
H 0.6
0.4
Fig 1.
Fig 2.
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