A Bayesian network (or a belief network) is a probabilistic graphical model that represents a set of
variables and their probabilistic independencies. For example, a Bayesian network could represent the
probabilistic relationships between diseases and symptoms. Given symptoms, the network can be used to compute
the probabilities of the presence of various diseases.
The following equations
:<math>3x+2y-z=1</math>:<math>2x-2y+4z=-2</math>:<math>-2x+y-2z=0</math>
form a system of three equations.
The following equations
form a system of three equations.
The following equations
{{NumBlk|:|<math>3x+2y-z=1</math>|1}}{{NumBlk|:|<math>2x-2y+4z=-2</math>|2}}{{NumBlk|:|<math>-2x+y-2z=0</math>|3}}
form a system of three equations.
The following equations
1
2
3
form a system of three equations.
The following equations
<divstyle="line-height: 0;">{{NumBlk|:|<math>3x+2y-z=1</math>|1}}{{NumBlk|:|<math>2x-2y+4z=-2</math>|2}}{{NumBlk|:|<math>-2x+y-2z=0</math>|3}}</div>
form a system of three equations.
The following equations
1
2
3
form a system of three equations.
The following equations
<divstyle="line-height: 0;">{{NumBlk||<math>3x+2y-z=1</math>|1}}{{NumBlk||<math>2x-2y+4z=-2</math>|2}}{{NumBlk||<math>-2x+y-2z=0</math>|3}}</div>
form a system of three equations.
The following equations
1
2
3
form a system of three equations.
The following equations
<divstyle="line-height: 0; margin-left: 1.6em;">{{NumBlk||<math>3x+2y-z=1</math>|1}}{{NumBlk||<math>2x-2y+4z=-2</math>|2}}{{NumBlk||<math>-2x+y-2z=0</math>|3}}</div>
form a system of three equations.
The following equations
:<math>3x+2y-z=1</math>::<math>2x-2y+4z=-2</math>:::<math>-2x+y-2z=0</math>
form a system of three equations.
The following equations
form a system of three equations.
The following equations
<divstyle="line-height: 0; margin-left: 1.6em;">{{NumBlk||<math>3x+2y-z=1</math>|1}}<divstyle="margin-left: 1.6em;">{{NumBlk||<math>2x-2y+4z=-2</math>|2}}<divstyle="margin-left: 1.6em;">{{NumBlk||<math>-2x+y-2z=0</math>|3}}</div></div></div>
form a system of three equations.
The following equations
1
2
3
form a system of three equations.
The following equations
<divstyle="line-height: 0;"><divstyle="margin-left: calc(1.6em * 1);">{{NumBlk||<math>3x+2y-z=1</math>|1}}</div><divstyle="margin-left: calc(1.6em * 2);">{{NumBlk||<math>2x-2y+4z=-2</math>|2}}</div><divstyle="margin-left: calc(1.6em * 3);">{{NumBlk||<math>-2x+y-2z=0</math>|3}}</div></div>
form a system of three equations.
<divstyle="line-height:0;">{{NumBlk|1=:|2=<math>a^2 + b^2 = (a + b i) (a - b i)</math>|3=1}}{{NumBlk|1=:|2=<math>a^2 - b^2 = (a + b) (a - b)</math>|3=2}}{{NumBlk|1=:|2=<math>e^{i x} = \cos x + i \sin x</math>|3=3}}{{NumBlk|1=:|2=<math>\sin^2 \theta + \cos^2 \theta = 1</math>|3=4}}{{NumBlk|1=:|2=<math>\sin(2 \theta) = 2 \sin\theta\cos\theta</math>|3=5}}</div>
Renders as
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Markup
<divstyle="line-height:0;">{{NumBlk|1=:|2=<math>a^2 + b^2 = (a + b i) (a - b i)</math>|3=1|LnSty=0.37ex dotted Gainsboro}}{{NumBlk|1=:|2=<math>a^2 - b^2 = (a + b) (a - b)</math>|3=2|LnSty=0.37ex dotted Gainsboro}}{{NumBlk|1=:|2=<math>e^{i x} = \cos x + i \sin x</math>|3=3|LnSty=0.37ex dotted Gainsboro}}{{NumBlk|1=:|2=<math>\sin^2 \theta + \cos^2 \theta = 1</math>|3=4|LnSty=0.37ex dotted Gainsboro}}{{NumBlk|1=:|2=<math>\sin(2 \theta) = 2 \sin\theta\cos\theta</math>|3=5|LnSty=0.37ex dotted Gainsboro}}</div>
Renders as
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Markup
<divstyle="line-height:0;">{{NumBlk|1=:|2=<math>a^2 + b^2 = (a + b i) (a - b i)</math>|3=1|LnSty=0.37ex dotted Gainsboro}}{{NumBlk|1=:|2=<math>a^2 - b^2 = (a + b) (a - b)</math>|3=2|LnSty=0.37ex none Gainsboro}}{{NumBlk|1=:|2=<math>e^{i x} = \cos x + i \sin x</math>|3=3|LnSty=0.37ex dotted Gainsboro}}{{NumBlk|1=:|2=<math>\sin^2 \theta + \cos^2 \theta = 1</math>|3=4|LnSty=0.37ex none Gainsboro}}{{NumBlk|1=:|2=<math>\sin(2 \theta) = 2 \sin\theta\cos\theta</math>|3=5|LnSty=0.37ex dotted Gainsboro}}</div>
Renders as
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Markup
<divstyle="line-height:0;"><divstyle="background-color: Beige;">{{NumBlk|1=:|2=<math>a^2 + b^2 = (a + b i) (a - b i)</math>|3=1}}</div><divstyle="background-color: none;">{{NumBlk|1=:|2=<math>a^2 - b^2 = (a + b) (a - b)</math>|3=2}}</div><divstyle="background-color: Beige;">{{NumBlk|1=:|2=<math>e^{i x} = \cos x + i \sin x</math>|3=3}}</div><divstyle="background-color: none;">{{NumBlk|1=:|2=<math>\sin^2 \theta + \cos^2 \theta = 1</math>|3=4}}</div><divstyle="background-color: Beige;">{{NumBlk|1=:|2=<math>\sin(2 \theta) = 2 \sin\theta\cos\theta</math>|3=5}}</div></div>
Renders as
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Markup
(mouse over the row you want to highlight)
{{row hover highlight}}{|class="hover-highlight"style="line-height:0; width: 100%; border-collapse: collapse; margin: 0; padding: 0;"|-|{{NumBlk|1=:|2=<math>a^2 + b^2 = (a + b i) (a - b i)</math>|3=1}}|-|{{NumBlk|1=:|2=<math>a^2 - b^2 = (a + b) (a - b)</math>|3=2}}|-|{{NumBlk|1=:|2=<math>e^{i x} = \cos x + i \sin x</math>|3=3}}|-|{{NumBlk|1=:|2=<math>\sin^2 \theta + \cos^2 \theta = 1</math>|3=4}}|-|{{NumBlk|1=:|2=<math>\sin(2 \theta) = 2 \sin\theta\cos\theta</math>|3=5}}|}
Renders as
(mouse over the row you want to highlight)
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Proof of hypothetical syllogism by constructive dilemma