Show that ρ（X，Y)=H（X|Y)+H（Y|X) has the above properties，and is therefore a metric．Note tha

Show that ρ(X，Y)=H(X|Y)+H(Y|X) has the above properties，and is therefore a metric．Note that ρ(X，Y) is the number of bits needed for X and to communicate their values to each other．

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更多“Show that ρ（X，Y)=H（X|Y)+H（Y|X)…”相关的问题

第1题

Entvopy rate．Let{Xi}be a discrete stationary stochastic process with entropy rate H∞（X)

Entvopy rate．Let{Xi}be a discrete stationary stochastic process with entropy rate H∞(X)。Show (1/n)H(Xn…X1|X0X-1…X-k)→H∞(x) for k=1，2，…．

Y=2X？

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第2题

Consider the following channel（is shown in Fig．3．26) is （1/2，0，1/2) an input distributi

Consider the following channel(is shown in Fig．3．26) is (1/2，0，1/2) an input distribution that achieves capacity？

Show that I(X；Y)=H(Y) - H(Z)．

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第3题

Verify that ρ（X；Y)can also be expressed as ρ（X，Y)=H（X)+H（Y) - 2I（X；Y) =H

Verify that ρ(X；Y)can also be expressed as ρ(X，Y)=H(X)+H(Y) - 2I(X；Y) =H(XY) - I(X；Y) =2H(XY) - H(X) - H(Y)

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第4题

已知一个空间不变相干成像系统的点扩散函数为h(x，y)，若系统输入为f(x，y)，则系统输出的计算式为( )。

A.f(x，y)·h(x，y)

B.h(x，y)·f(x，y)

C.f(x，y)/h(x，y)

D.h(x，y)/f(x，y)

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第5题

Inequalities．Let X，Y and Z be a discrete joint random variables．Prove the validity of the

following inequalities and find condition for equality． (1)H(XY|Z)≥H(X|Z) (2)I(XY；Z)≥I(X；Z) (3)I(X；Z|Y)≥I(Z；Y|X) - I(Z；Y)+I(X；Z) (4)H(XYZ) - H(XY)≤H(XZ) - H(X)

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第6题

已知X和Y都是取值于{0，1}的一进制随机变量，P（X=0)=p。还已知P（X≠Y f X)=ε。求概率P（Y=1)，熵H（X)，H（

已知X和Y都是取值于{0，1}的一进制随机变量，P(X=0)=p。还已知P(X≠Y f X)=ε。求概率P(Y=1)，熵H(X)，H(Y)，H(Y|X以及互信息I(X；Y)。假设ε给定，p可变，求能使I(X；Y)最大的p。

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第7题

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

Using Venn diagrcuns(维拉图)，we can see that mutual information common to three random variable X，Y and Z should be defined by I(X；Y；Z)=I(X；Y) - I(X；Y|Z) This quantity is symmetric in X，Y and Z，despite the preceding asymmetric define．Unfortunately，I(X；Y；Z)is not nesessarily nonnegative．Find X，Y，Z such that I(X；Y；Z)＜0,and Prove the following two identities： I(X；Y；Z)=H(XYZ) - H(X) - H(Y) - H(Z)+I(X；Y)+I(Y；Z)+I(Z；X) I(X；Y；Z)=H(XYZ) - H(XY) - H(YZ) - H(ZX)+H(X)+H(Y)+H(Z) The first identity can be understood using the Venn diargram analogy for entropy and mutual lnlormatlon．The second identity follows easily from the first．

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第8题

X是n维连续型随机矢量，Y=AX是X的线性变换，并且A是一个n×n的非奇异矩阵，证明h（Y)=log2|det（A)|+h（X)。

X是n维连续型随机矢量，Y=AX是X的线性变换，并且A是一个n×n的非奇异矩阵，证明h(Y)=log₂|det(A)|+h(X)。

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第9题

已知H（Y|X)=0，求证，p（x)＞0，只存在一个y使得p（xy)＞0。

已知H(Y|X)=0，求证，p(x)＞0，只存在一个y使得p(xy)＞0。