有一信源输出X∈{0，1，2}，其概率为p0=1／4，p1=1／4，p2=1／2。设计两个独立实验去观察它，其结果分别为Y1

dent． let ρ=1 - H(X1|X2)/H(X1) (1)Show ρ=I(X1；X2)／H(X1) (2)Show 0≤ρ≤1 (3)When is ρ=0? (4)When is ρ=1?

(XY) - I(X；Y) =2H(XY) - H(X) - H(Y)

t ρ(X，Y) is the number of bits needed for X and to communicate their values to each other．

e variance of I(x；y)=0．Prove that the input assignment achieves channel capacity．

;0 and VAR[I(x；y)]=0．Calculate I(X；Y)．

(xy)=αP(x)P(y)

acity?

With 0，1，as both input and output，the transition probabilites for 0 to 0 and 1 are 1-ε and ε respectively while those for 1 to 1 and 0 are 1-δ and δ respectively．Assuming that 0<ε<1 and 0<δ<1，find the capacity of the channel．

Suppose that the output of the first channel is connected directly to the input of the second with no processing between： What is the capacity of the composite channel?

nt．