A municipal bond service has three rating categories (A, B, and C). Suppose that

Question

A municipal bond service has three rating categories (A, B, and C). Suppose that in the past year, of the municipal bonds issued thoughout a country, 50% were rated A, 20% were rated B, and 30% were rated C. Of the municipal bonds rated A, 60% were issued by cities, 10% by suburbs, and 30% by rural areas. Of the municipal bonds rated B, 50% were issued by cities, 30% by suburbs, and 20% by rural areas. Of the municipal bonds rated C, 90% were issued by cities, 5% by suburbs, and 5% by rural areas. Complete (a) through (c) below. a. If a new municipal bond is to be issued by a city, what is the probability that it will receive an A rating? b. What proportion of municipal bonds are issued by cities? c. What proportion of municipal bonds are issued by suburbs?

Explanation / Answer

from above information;joint probability distribution in different scenario is given below:

probabilty that municipal bond issued by a city=from city and rated A+from city and rated B+from city and rated c

=0.5*0.6+0.2*0.5+0.3*0.9=0.67

a) therefore probabilty that bond recieve A rating given from city=0.5*0.6/0.67=0.4478

b) proportion of municipal bonds are issued by cities=0.67

c)proportion of municipal bonds are issued by suburbs=0.125

cities suburbs rural Total A 0.3 0.05 0.15 0.5 B 0.1 0.06 0.04 0.2 C 0.27 0.015 0.015 0.3 Total 0.67 0.125 0.205 1

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