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3. Bayesian Reason ing Consider the following Bayesian network. A Further suppose that this network contains the follow...
[10 Points] Assume the Bayesian belief network for the diagnosis of car's electrical system. Battery Radio Lights I...
[10 Points] Assume the Bayesian belief network for the diagnosis of car's electrical system. Battery Radio Lights Ignition Gas Engine starts Car moves Assume that all variables in the network are binary with True and False values. a. The belief network structure encodes conditional and marginal independences in graphical terms. Give at least three examples of conditional and one example of marginal independences encoded in the network structure. b. Assume that all variables in the network are binary (have two...
Consider the following Bayesian network for detecting credit-card fraud: pla 30)- 0.25 p(a-30-50) 0.40 p(s-male)-0.5 p(f-yes) 0.00001 Fraud Sex Jewelry Jas PV-veslf-yes, a= *s= *) = 0.05 PV-yesy-no,...
Consider the following Bayesian network for detecting credit-card fraud: pla 30)- 0.25 p(a-30-50) 0.40 p(s-male)-0.5 p(f-yes) 0.00001 Fraud Sex Jewelry Jas PV-veslf-yes, a= *s= *) = 0.05 PV-yesy-no, a=<30,s-male) = 0..000 I pi-yeslf no,a-30-50,s-male)- 0.0004 pj-yeslf no,a-50,s-male) 0.0002 p-yeslf no,a-<30,s-female) -0.0005 p(j=ves-no,a-30-50's-female) = 0.002 p(g yeslf-yes)-0.2 plg yes no 0.01 Arcs (arrows) are drawn from cause to effect, e.g., the stolen card used for either gas or jewelry. It means that the current effect is dependent only on its parent...
Problem 2 Consider the following Bayesian network for detecting credit-card fraud Pa30) 0.25 pla-30-50) 0.40 p(s-male)-0.5...
Problem 2 Consider the following Bayesian network for detecting credit-card fraud Pa30) 0.25 pla-30-50) 0.40 p(s-male)-0.5 p(f-yes) 0.00001 Fraud Sex Age Jewelry Gas plg yeslf yes)-0.2 pg-yesy-no) = 0.01 pi yeslfyes,a s0.05 pi yesf no,a 30,s-male) 0.0001 pi yeslf-no,a 30-50,s-male) 0.0004 PV=yeslf-no,a=>50,s= male) = 0.0002 pi yeslf-no,a 30,s female) 0..0005 py-yeslf-no,a-30-50.5 emale) = 0.002 pi yesf no,a 50,s female) 0.001 Arcs (arrows) are drawn from cause to effect, eg., the stolen card used for either gas or jewelry. It means...
Given the following Bayesian network, where all random variables have Boolean values (true or fal...
Given the following Bayesian network, where all random variables have Boolean values (true or false), compute the probability of D being true, given that A is true. That is, compute P(D-true |A-true) AP(A) 0.7 P(B IA) 0.2 P(B 1-A)-0.5 P(C I A)-0.7 PCI-A)-0.25 P(D IBAC)-0.3 P(D I-BAC)-0.1
Given the following Bayesian network, where all random variables have Boolean values (true or false), compute the probability of D being true, given that A is true. That is, compute P(D-true |A-true) AP(A)...
Problem 2 Consider the following Bayesian network for detecting credit-card fraud: pla <30)-0.25 pla-30-50)-0.40 ps-male)-o.s p(-yes)-0.00001 Fraud Age Sex Jewelry pig yeslf-yes)-0.2 pig yeslf...
Problem 2 Consider the following Bayesian network for detecting credit-card fraud: pla <30)-0.25 pla-30-50)-0.40 ps-male)-o.s p(-yes)-0.00001 Fraud Age Sex Jewelry pig yeslf-yes)-0.2 pig yeslf-no)-0.01 pU yeslf-no,a 30,s-male)-0.0001 PV=yesV-no,a-30-50.5-male)-0.0004 PV "yes f-no,a =>50.5-male) = 0.0002 pf yesfeno,a 30,s female)-0.0005 PU =yes ir-no,a-30-50.5-emale) = 0.002 PV=yesy-noa->50.5-female) = 0.001 Arcs (arrows) are drawn from cause to effect, eg., the stolen card used for either gas or jewelry. It means that the current effect is dependent only on its parent node, which represents its...
Problem 2 Consider the following Bayesian network for detecting credit-card fraud Pla-<30)-0.25 p(a-30-50) 0.40 pf-yes)-0.00001 p(s-male-0.5 Fraud Sex Jewe Gas pi-yesf yes,a 0.0s po yeslf no,a...
Problem 2 Consider the following Bayesian network for detecting credit-card fraud Pla-<30)-0.25 p(a-30-50) 0.40 pf-yes)-0.00001 p(s-male-0.5 Fraud Sex Jewe Gas pi-yesf yes,a 0.0s po yeslf no,a-30,s-male)-0.0001 pG yeslf-no,a-30-50,s-male) -0.0004 po yeslf no,a->50,s-male)-0.0002 po yesf no,a 30,s Jemale)-0.0005 pi yesf no,a 30-50,s female) 0.002 pi yes no,a >50,s female)-0.00 p(g yesf yes) 0.2 pg-yes|f=no) = 0.01 Arcs (arrows) are drawn from cause to effect, e.g., the stolen card used for either gas or jewelry. It means that the current effect is...
Problem 2 Consider the following Bayesian network for detecting credit-card fraud Pa30) 0.25 pla-30-50) 0.40 p(s-male)-0.5 p(f-yes) 0.00001 Fraud Sex Age Jewelry Gas plg yeslf yes)-0.2 pg-yesy-no)...
Problem 2 Consider the following Bayesian network for detecting credit-card fraud Pa30) 0.25 pla-30-50) 0.40 p(s-male)-0.5 p(f-yes) 0.00001 Fraud Sex Age Jewelry Gas plg yeslf yes)-0.2 pg-yesy-no) = 0.01 pi yeslfyes,a s0.05 pi yesf no,a 30,s-male) 0.0001 pi yeslf-no,a 30-50,s-male) 0.0004 PV=yeslf-no,a=>50,s= male) = 0.0002 pi yeslf-no,a 30,s female) 0..0005 py-yeslf-no,a-30-50.5 emale) = 0.002 pi yesf no,a 50,s female) 0.001 Arcs (arrows) are drawn from cause to effect, eg., the stolen card used for either gas or jewelry. It means...
81. Consider the function g(x, y) given by, 1 1.52.53 11/4 0 0 0 2 0...
81. Consider the function g(x, y) given by, 1 1.52.53 11/4 0 0 0 2 0 1/8 0 0 y 3 0 1/4 0 0 4 0 0 1/4 0 5 00 0 1/8 and complete / determine the following: (a) Show that g(x, y) satisfies the properties of a joint pmf. (See Table in ?6.0.1.) (b) P(X < 2.5,Y < 3) (c) P(X < 2.5) (d) P(Y < 3) (e) P(X> 1.8, Y> 4.7) (f) E[X], EY], Var(X), Var(Y)...
17. Consider the Bayesian network drawn below A P(A true) 0.4 P(B-true | A-false)0.9 D P(B-true...
17. Consider the Bayesian network drawn below A P(A true) 0.4 P(B-true | A-false)0.9 D P(B-true | A-true0.3 P(C-true) 0.7 P(D true | B-false and C-false)0.8 P(D-true | B-false and C-true) 0.3 P(D-true | B-true and C-false) 0.5 P(D-true | B-true and C-true)0.1 Show your work for the following calculations a) Compute P(A true and B -false and C- true and D -false) b) Compute P(D true | A -false and B-true and C-false) cCompute P(A true | B -false...
For questions 5-8, consider the following experiment: Suppose the location of a particle in the p...
For questions 5-8, consider the following experiment: Suppose the location of a particle in the plane is restricted to be within the region of the first quadrant enclosed by y = 0, y = 2, and 1-1 and that the z and y coorlinates of the point are d(scribed by the jointly continuous random variables X and Y, respectively, with joint pdf Uz, y) = cryl(0,1) (z)10.ェ2)(y) 5. Given this joint pdf, (a) Find the value of c that makes...
[10 Points] Assume the Bayesian belief network for the diagnosis of car's electrical system. Battery Radio Lights Ignition Gas Engine starts Car moves Assume that all variables in the network are binary with True and False values. a. The belief network structure encodes conditional and marginal independences in graphical terms. Give at least three examples of conditional and one example of marginal independences encoded in the network structure. b. Assume that all variables in the network are binary (have two...
Consider the following Bayesian network for detecting credit-card fraud: pla 30)- 0.25 p(a-30-50) 0.40 p(s-male)-0.5 p(f-yes) 0.00001 Fraud Sex Jewelry Jas PV-veslf-yes, a= *s= *) = 0.05 PV-yesy-no, a=<30,s-male) = 0..000 I pi-yeslf no,a-30-50,s-male)- 0.0004 pj-yeslf no,a-50,s-male) 0.0002 p-yeslf no,a-<30,s-female) -0.0005 p(j=ves-no,a-30-50's-female) = 0.002 p(g yeslf-yes)-0.2 plg yes no 0.01 Arcs (arrows) are drawn from cause to effect, e.g., the stolen card used for either gas or jewelry. It means that the current effect is dependent only on its parent...
Problem 2 Consider the following Bayesian network for detecting credit-card fraud Pa30) 0.25 pla-30-50) 0.40 p(s-male)-0.5 p(f-yes) 0.00001 Fraud Sex Age Jewelry Gas plg yeslf yes)-0.2 pg-yesy-no) = 0.01 pi yeslfyes,a s0.05 pi yesf no,a 30,s-male) 0.0001 pi yeslf-no,a 30-50,s-male) 0.0004 PV=yeslf-no,a=>50,s= male) = 0.0002 pi yeslf-no,a 30,s female) 0..0005 py-yeslf-no,a-30-50.5 emale) = 0.002 pi yesf no,a 50,s female) 0.001 Arcs (arrows) are drawn from cause to effect, eg., the stolen card used for either gas or jewelry. It means...
Given the following Bayesian network, where all random variables have Boolean values (true or false), compute the probability of D being true, given that A is true. That is, compute P(D-true |A-true) AP(A) 0.7 P(B IA) 0.2 P(B 1-A)-0.5 P(C I A)-0.7 PCI-A)-0.25 P(D IBAC)-0.3 P(D I-BAC)-0.1
Given the following Bayesian network, where all random variables have Boolean values (true or false), compute the probability of D being true, given that A is true. That is, compute P(D-true |A-true) AP(A)...
Problem 2 Consider the following Bayesian network for detecting credit-card fraud: pla <30)-0.25 pla-30-50)-0.40 ps-male)-o.s p(-yes)-0.00001 Fraud Age Sex Jewelry pig yeslf-yes)-0.2 pig yeslf-no)-0.01 pU yeslf-no,a 30,s-male)-0.0001 PV=yesV-no,a-30-50.5-male)-0.0004 PV "yes f-no,a =>50.5-male) = 0.0002 pf yesfeno,a 30,s female)-0.0005 PU =yes ir-no,a-30-50.5-emale) = 0.002 PV=yesy-noa->50.5-female) = 0.001 Arcs (arrows) are drawn from cause to effect, eg., the stolen card used for either gas or jewelry. It means that the current effect is dependent only on its parent node, which represents its...
Problem 2 Consider the following Bayesian network for detecting credit-card fraud Pla-<30)-0.25 p(a-30-50) 0.40 pf-yes)-0.00001 p(s-male-0.5 Fraud Sex Jewe Gas pi-yesf yes,a 0.0s po yeslf no,a-30,s-male)-0.0001 pG yeslf-no,a-30-50,s-male) -0.0004 po yeslf no,a->50,s-male)-0.0002 po yesf no,a 30,s Jemale)-0.0005 pi yesf no,a 30-50,s female) 0.002 pi yes no,a >50,s female)-0.00 p(g yesf yes) 0.2 pg-yes|f=no) = 0.01 Arcs (arrows) are drawn from cause to effect, e.g., the stolen card used for either gas or jewelry. It means that the current effect is...
Problem 2 Consider the following Bayesian network for detecting credit-card fraud Pa30) 0.25 pla-30-50) 0.40 p(s-male)-0.5 p(f-yes) 0.00001 Fraud Sex Age Jewelry Gas plg yeslf yes)-0.2 pg-yesy-no) = 0.01 pi yeslfyes,a s0.05 pi yesf no,a 30,s-male) 0.0001 pi yeslf-no,a 30-50,s-male) 0.0004 PV=yeslf-no,a=>50,s= male) = 0.0002 pi yeslf-no,a 30,s female) 0..0005 py-yeslf-no,a-30-50.5 emale) = 0.002 pi yesf no,a 50,s female) 0.001 Arcs (arrows) are drawn from cause to effect, eg., the stolen card used for either gas or jewelry. It means...
81. Consider the function g(x, y) given by, 1 1.52.53 11/4 0 0 0 2 0 1/8 0 0 y 3 0 1/4 0 0 4 0 0 1/4 0 5 00 0 1/8 and complete / determine the following: (a) Show that g(x, y) satisfies the properties of a joint pmf. (See Table in ?6.0.1.) (b) P(X < 2.5,Y < 3) (c) P(X < 2.5) (d) P(Y < 3) (e) P(X> 1.8, Y> 4.7) (f) E[X], EY], Var(X), Var(Y)...
17. Consider the Bayesian network drawn below A P(A true) 0.4 P(B-true | A-false)0.9 D P(B-true | A-true0.3 P(C-true) 0.7 P(D true | B-false and C-false)0.8 P(D-true | B-false and C-true) 0.3 P(D-true | B-true and C-false) 0.5 P(D-true | B-true and C-true)0.1 Show your work for the following calculations a) Compute P(A true and B -false and C- true and D -false) b) Compute P(D true | A -false and B-true and C-false) cCompute P(A true | B -false...
For questions 5-8, consider the following experiment: Suppose the location of a particle in the plane is restricted to be within the region of the first quadrant enclosed by y = 0, y = 2, and 1-1 and that the z and y coorlinates of the point are d(scribed by the jointly continuous random variables X and Y, respectively, with joint pdf Uz, y) = cryl(0,1) (z)10.ェ2)(y) 5. Given this joint pdf, (a) Find the value of c that makes...
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