Théorie de l'information - 4
mardi 13 mai 2014
15:20
Exercice 1
P(Y|X) = 
X/Y
Y1 = 0
Y2 = 1
Y3 = -1
X1 = 0
0.7
0.2
0.1
X2 = 1
0.3
0.6
0.1
===> P(X,Y) = 
X/Y
0
1
-1
Px
0
0.7*0.5
0.35
0.2*0.5
0.1
0.1*0.5
0.05
0.35+0.1+0.05
0.5
1
0.3*0.5
0.15
0.6*0.5
0.3
0.1*0.5
0.05
0.5
Px
0.35+0.15
0.5
0.1+0.3
0.4
0.05+0.05
0.1
 P(X|Y)=
X/Y
0
1
-1
0
0.35/0.5
0.7
0.1/0.4
0.75
0.05/0.1
0.5
1
0.15/0.5
0.3
0.3/0.4
0.75
0.05/0.1
0.5 
Distribution conditionelle
Distribution conditionelle
Distribution Marginale
H(X) = log2(2) = 1 bit/symbole
H(Y) = -0.5*log2(0.5) -0.4*log2(0.4)-0.1*log2(0.1) = 1.36 bits/symbole
H(X,Y) = 2.23 bits/Symbole
H(X|Y) = 0.86 bits/symb
H(Y|X) = 1.23 bits/sy
I(X,Y) = I(Y,X) = H(X) - H(X|Y)
  = H(Y) - H(Y|X)
  = 0.13 bit/symbole
Exercice 2 
Non symétrique.
P(Y|X) = 
X/Y
Y1 = 0
Y2 = -1
Y3 = 1
X1 = 0
0.8
0.2
0
X2 = 1
0
0.2
0.8