A measure of correlation．Let X1和X2 be identically distributed，but not necessarily indepen

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？

查看答案

如搜索结果不匹配，请联系老师获取答案

您可能会需要：

重置密码查看订单联系客服

安装上学吧APP，拍照搜题省时又省心！

更多“A measure of correlation．Let X…”相关的问题

第1题

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)

点击查看答案

第2题

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

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

点击查看答案

第3题

Suppose a DMC has the property that for some input assignment P(x)>0，x∈A={0，1，…，k-1}，th

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

点击查看答案

第4题

For each of the Channels in Fig．3．22，find a probabilty assignment P(x) such that I(X；Y)>

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

点击查看答案

第5题

Express I(X；Y)in term of α and interpret the special case α=1．

点击查看答案

第6题

Prove that VAR[I(x；y)]=0 iff there is a constant α such that，for all x，y with P(xy)>0，P

(xy)=αP(x)P(y)

点击查看答案

第7题

Suppose that a decoder／encoder(a recoder)is allowed between the channels： What is the cap

acity?

点击查看答案

第8题

With 0，1，as both input and output，the transition probabilites for 0 to 0 and 1 are 1-ε

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?

点击查看答案

第9题

Find the capacity in terms of H(Z)and find the maximizing input probability assignme

nt．

点击查看答案

第10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)．

点击查看答案