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...

• 2

This preview shows page 1 - 2 out of 2 pages.

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.

Want to read both pages?

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....
View Full Document

• Spring '06
• Staff
• Economics, Logic, English-language films, Following, Equals sign

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern

Stuck? We have tutors online 24/7 who can help you get unstuck.
Ask Expert Tutors You can ask You can ask You can ask (will expire )
Answers in as fast as 15 minutes