Compute the effective source entropy $${ } ^ { \wedge } \mathrm { H } _ { \mathrm { S } } ( \mathrm { x } . \mathrm { xx } \text { bits/symbol) }$$ of the source producing following 20-symbol sequence
AAABAAACAAADAAAEAAAF

Name: Compute the effective source entropy \[{ } ^ { \wedge } \mathrm { H } _ { \mathrm { S } } ( \mathrm { x } . \mathrm { xx } \text { bits/symbol) }\] of the source producing following 20-symbol sequence AAABAAACAAADAAAEAAAF
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\mathrm { P } _ { \mathrm { e } } [ \mathrm { A } ] = 15 / 20 = 0.75 , \mathrm { P } _ { \mathrm { e } } [ \mathrm { B } ] = 1 / 20 = 0.05 , \mathrm { P } _ { \mathrm { e } } [ \mathrm { C } ] = 0.05 , \mathrm { P } _ { \mathrm { e } } [ \mathrm { D } ] = 0.05 , \mathrm { P } _ { \mathrm { e } } [ \mathrm { E } ] = 0.05 , \mathrm { P } _ { \mathrm { e } } [ \mathrm { F } ] = 0.05

{ } ^ { \wedge } \mathrm { H } _ { \mathrm { S } } = - \sum \mathrm { P } _ { \mathrm { e } } \left[ \mathrm { X } _ { \mathrm { i } } ight] \log _ { 2 } \mathrm { P } _ { \mathrm { e } } \left[ \mathrm { X } _ { \mathrm { i } } ight] = - ( 0.75 ) ( - 0.42 ) - ( 5 ) ( 0.05 ) ( - 22.02 ) = 1.39 \mathrm { bits } / ext { symbol. }

Compute the Effective Source Entropy ∧HS(x.xx bits/symbol) { } ^ { \wedge } \mathrm { H } _ { \mathrm { S } } ( \mathrm { x } . \mathrm { xx } \text { bits/symbol) }∧HS​(x.xx bits/symbol)

Compute the Effective Source Entropy ${ } ^ { \wedge } \mathrm { H } _ { \mathrm { S } } ( \mathrm { x } . \mathrm { xx } \text { bits/symbol) }$