もっと詳しく

Characterization: the fourth axiom had no sense: typo fixed


← Previous revision Revision as of 22:35, 19 October 2021
Line 104: Line 104:
 
# {{math|I(”p”) ≥ 0}}: information is a [[non-negative]] quantity.
  
# {{math|I(”p”) ≥ 0}}: information is a [[non-negative]] quantity.
 
# {{math|I(1) {{=}} 0}}: events that always occur do not communicate information.
  
# {{math|I(1) {{=}} 0}}: events that always occur do not communicate information.
−
# {{math|I(”p”<sub>1</sub>, ”p”<sub>2</sub>) {{=}} I(”p”<sub>1</sub>) + I(”p”<sub>2</sub>)}}: the information learned from [[independent events]] is the sum of the information learned from each event.
 +
# {{math|I(”p”<sub>1</sub>·”p”<sub>2</sub>) {{=}} I(”p”<sub>1</sub>) + I(”p”<sub>2</sub>)}}: the information learned from [[independent events]] is the sum of the information learned from each event.
   
 
Given two independent events, if the first event can yield one of {{math|”n”}} [[equiprobable]] outcomes and another has one of {{math|”m”}} equiprobable outcomes then there are {{math|”mn”}} equiprobable outcomes of the joint event. This means that if {{math|log<sub>2</sub>(”n”)}} bits are needed to encode the first value and {{math|log<sub>2</sub>(”m”)}} to encode the second, one needs {{math|log<sub>2</sub>(”mn”) {{=}} log<sub>2</sub>(”m”) + log<sub>2</sub>(”n”)}} to encode both.
  
Given two independent events, if the first event can yield one of {{math|”n”}} [[equiprobable]] outcomes and another has one of {{math|”m”}} equiprobable outcomes then there are {{math|”mn”}} equiprobable outcomes of the joint event. This means that if {{math|log<sub>2</sub>(”n”)}} bits are needed to encode the first value and {{math|log<sub>2</sub>(”m”)}} to encode the second, one needs {{math|log<sub>2</sub>(”mn”) {{=}} log<sub>2</sub>(”m”) + log<sub>2</sub>(”n”)}} to encode both.