Using Venn diagrcuns（维拉图)，we can see that mutual information common to three random var

N．Each sequences an even number of 1’S has probabilitv 2-(N-1) and each sequences with an odd number of 1’s has probability zero．Find the average mutual informations I(X1；X2)，I(X3；X2|X1)，…，I(XN；XN-1|X1X2…XN-2) Check your result for N=3．

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∈{0，1}和Y2∈{0，1}。已知条件概率为：

求：(1)I(X；Y1)和I(X；Y2)，并判断哪个实验好些。 (2)I(X；Y1Y2)，并计算做Y1和Y2两个实验比做Y1或Y2中的一个实验各可多得多少关于X的信息。 (3)I(X；Y1|Y2)和I(X；Y2|Y1)，并解释它们的含义。

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?