Untitleddocument - 1 The generalized product rule Pr(A,B|K = Pr(A|B,K)Pr(B,K come from the following set of rules a Pr(A,B|K = Pr(A|B,K)Pr(B,K b

# Untitleddocument - 1 The generalized product rule Pr(A,B|K...

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1. The generalized product rule: Pr(A,B|K) = Pr(A|B,K)Pr(B,K) come from the following set of rules: a. Pr(A,B|K) = Pr(A|B,K)Pr(B,K) b. Pr(A,B,K)/Pr(K) = Pr(A,B,K)/Pr(B,K) * Pr(B,K)/Pr(K) c. Pr(A,B,K)/Pr(K) = Pr(A,B,K)/Pr(K) Thereby proving the generalized product rule. The generalized bayes rule is: P(A | B, K) = P(B | A, K)P(A | K)/P(B | K) comes from the following set of rules: a. 2. We have a set of known information listed below: Pr(oil) Pr(Natural Gas) Pr(neither) Pr(positive | oil) Pr(positive | natural gas) Pr(positive | neither) Now we need to find Pr(oil | positive) which is equal to: Pr(positive | oil)*Pr(oil)/Pr(positive) This give us: 0.83. 3. We have for alpha1 that there are 9 objects out of 13 total objects hence we have 9/13. For alpha2 we have 8 objects out of 13 so it is 8/13. For alpha3 we have Pr(square ^(one v black))/Pr(one v black) Therefore we have 7/13*13/11 = 7/11 World Black Square One Pr 1 true true true 2/13 2 true true false 4/13 3 true false true 1/13 4 true false false  #### You've reached the end of your free preview.

Unformatted text preview: 2/13 5 false true true 1/13 6 false true false 1/13 7 false false true 1/13 8 false false false 1/13 From teh above table we can see that the values of the alphas hold. Now the following sentences show that alpha is independent from beta given that gamma is true: a.Given that gamma= ~black, alpha=square and beta=one are independent. b.Given taht gamme=~black, alpha=~one and beta=square are independent. 4.The markovian assumptions are: I(A, nil, {B,E}) I(B,nil, {A,C}) I(C,A,{B,D,E}) I(D,{A,B},{C,E}) I(E, B,{A,C,D,F,G}) I(F,{C,D},{A,B,E}) I(G,F,{A,B,C,D,E,H}) I(H,{E,F},{A,B,C,D,G}) B. i. False ii.True. iii. False C. Pr(a|b,c,d,e,f,g,h)*Pr(b|c,d,e,f,g,h)*Pr(c|d,e,f,g,h)*Pr(d|e,f,g,h)*Pr(e|f,g,h)*Pr(f|g,h)*Pr(g|h)*Pr(h) D. Pr(A=0,B=0) = Pr(A=0)*Pr(B=0) = 0.24 Pr(E=1,A=1) = Pr(E=1,A=1)/Pr(A=1) As we continue to simplify (Pr(A=1)*Pr(E=1))/Pr(A=1) = Pr(E=1) = Pr(E=1,B=0) + Pr(E=1,B=0) = Pr(E=1,B=0)*Pr(B=0) + Pr(E=1,B=1)/Pr(B=1) This value is equal to 0.34....
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