Week 3 Homework problem 10 and 11

Week 3 Homework problem 10 and 11 - From Equation 4.9 =...

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Homework problem 10 Given: P(B) = 0.1, P(A|B) = 0.7, P(B’) = 0.9, P(A|B’) = 0.4 Find P(B|A) From equation 4.4: = ( ) ( ) PBA P A and B P A and = ( ) ( ) PAB P A and B P B From equation 4.6: = * = . * . = . PA and B PAB PB 0 7 0 1 0 07 From equation 4.2 = + ( ) PA PA and B P A and B' Then = * + * = . * . + . * . = . PA PAB PB PAB' PB' 0 7 0 1 0 4 0 9 0 43 Combining the two: = * = . * . . = . PBA PAB PBPA 0 7 0 10 43 0 163
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Problem 11 Let the bond ratings be represented by A, B and C and let the issuing municipalities be represented by Ct, S, and R Given: P(A) = 0.60, P(Ct|A) = 0.4, P(Ct|B) = 0.5, P(Ct|C) = 0.7, P(B) = 0.10, P(S|A) = 0.5, P(S|B) = 0.4, P(S|C) = 0.15, P(C) = 0.30, P(R|A) = 0.1, P(R|B) = 0.1, P(R|C) = 0.15, Part a) What is the probability that a bond will receive an A rating given it is issued by a city?
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Unformatted text preview: From Equation 4.9 = * * + * + * PACt PCtA PAPCtA PA PCtB PB PCtC PC All of these are given = . * . . * . + . * . +( . * . )= . PACt 0 4 0 60 4 0 6 0 5 0 1 0 7 0 3 0 48 Part b) What portion of bonds are issued by cities? You should recognize that the denominator: * + * + * = ( ) PCtA PA PCtB PB PCtC PC P Ct = . * . + . * . + . * . = . PCt 0 4 0 6 0 5 0 1 0 7 0 3 0 5 Part c) What portin of bonds are issued by suburbs? Similar to part b = * + * + * PS PSA PA PSB PB PSC PC = . * . + . * . + . * . = . PS 0 5 0 6 0 4 0 1 0 15 0 3 0 385...
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Week 3 Homework problem 10 and 11 - From Equation 4.9 =...

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