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Conditional mutual information．Consider a sequences of N binary random variables X1，X2，…，X

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．

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发布时间：2022-12-04

更多“Conditional mutual information．Consider a sequences of N binary random variables X1，X2，…，X”相关的问题

第1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2题

Not long ago, I had my first on-line chat. I thought it would be【C1】______because I have h

eard so many people describe it in that way. But it was, disappointingly, quite an unpleasant【C2】______. On line I met a man【C3】______said he was a manager in a big company in Dalian. We chatted pleasantly first, then exchanged e-mail adresses in order to keep in touch in the future.【C4】______, he sent me an e-mail. When I opened it, I found, to my surprise, a detailed(详细的)self-introduction including age,【C5】______, weight, habits and future plans. It was an advertisement for a dating(约会)service! I was hurt【C6】______felt rather angry. When I told a veteran(有经验的)Internet surfer(网民)of my experience, he said it was not uncommon. I was【C7】______. The Web provides such a nice, large place to make friends, why do some people【C8】______it？ The relationship between one another should be mutual(互助的)politeness and respect. Online we cant see one another s physical form, but we are talking through our【C9】______. Such tricks as the one I met are not polite at all. Since the Web belongs to everyone, every user has a duty to keep a friendly and polite atmosphere(氛围). We need【C10】______honesty and respect on-line.

【C1】

A．exciting

B．disappointing

C．surprising

D．frightening

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第3题

Define the conditional entropy HL／L（U)=（1/L)H（U2L…L+1|UL…U1) for a discrete stationary sou

Define the conditional entropy HL／L(U)=(1/L)H(U2L…L+1|UL…U1) for a discrete stationary source of alphabet size K．

Prove that HL／L(U)is nonicreasing with L．

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第4题

A gloomy afternoon saw me taking my routine path through that construction site. For the w

alker s convenience, a set of stone steps had been built, which were fairly steep. That was the place I found myself behind a husband and wife climbing up the steps with each other s support. The couple seemed to be farmers in their forties. The wife in a red coat was walking with a stick, an empty trouser leg swaying below. With one hand on his shoulder, she leaned almost entirely on her husband, who carefully kept balance with her and carried her other stick. They limped(跛行)their way upward with great difficulty. My curiosity urged me to overtake them and look back over my shoulder secretly. The glance sent a shiver through me, which produced a sensation I had never experienced before. The husband himself was also disabled—blind in both eyes! What struck me even more was the smile they both wore on their faces, such a happy smile as could only be seen from brides and bridegrooms. With few words between them, they smilingly helped each other struggle upwards. Then I noticed there were patches on their clothes, and their cloth shoes were homemade, worn-out but tidy. How could such sweet smiles reconcile(使和谐)with the patched clothing or the physical handicap？ I got quite puzzled. When they advanced far ahead I still couldn t tear my eyes away from them, I was moved and my heart filled with admiration. At that moment I suddenly realized how superficial my idea of happiness had been! To me it had always been associated with wealth, fame and power, the poor and the lowly having no share of it. However, happiness can be found in very ordinary life. I witnessed it on the weather-beaten faces of the husband and wife who had shared happiness and misfortune together. There is always happiness when there is an unfailing mutual support between two persons in love.

How did the husband and wife climb up the steps？

A．They didn" t help each other.

B．They climbed up the steps with ease.

C．They limped their way upward with each other" s support.

D．They climbed up the steps depending on a stick.

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第5题

Important business will result ______ our mutual understanding and cooperation. A．in B．from C．

Important business will result ______ our mutual understanding and cooperation.

A．in B．from C．of D．on

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第6题

This Agreement is ______ into between the parties concerned on the basis of equality and mutual bene

A.A.entered

B.B.become

C.C.come

D.D.turned

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第7题

惟有相互了解，才能增进信任，加强合作。

A.It is mutual understanding that makes us build trust and promote cooperation with one another.

B.Only mutual understanding can lead to trust and cooperation with other countries.

C.Mutual understanding is the only one factor for us to build trust and promote cooperation with one another.

D.Without mutual understanding, it would be impossible for countries to build trust and promote cooperation with one another.

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第8题

We desire to establish _____ beneficial business relations.

A.mutually

B.mutual

C.equal

D.inequally

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第9题

Both sides are working for the _____ of mutual relationship.

A.action

B.activity

C.raise

D.promotion

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第10题

This Agreement is entered into ______ the parties concerned ______ the basis of equality and mutual

benefit to develop business ______ terms and conditions mutually agreed upon as follows: .

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第11题

WHEREAS Party B is ______ the real estate business, and the two parties are ______ consideration of

the mutual conveyances' and agree to enter ______ this Contract under the terms and conditions set forth as follows:

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