Express I(X;Y)in term of α and interpret the special case α=1.
第1题
(xy)=αP(x)P(y)
第2题
acity?
第3题
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?
第5题
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).
第7题
2,而其他概率值不变。试证明由此所得新的概率空间的熵是增加的,并用熵的物理意义加以解释。
第10题
同时扔一对均匀的骰子,当得知“两骰子面朝上点数之和为2”或“面朝上点数之和为8”或“骰子面朝上点数是3和4”时,试问这三种情况分别获得多少信息量?
若仅有质点A,求A落入任一个格的平均自信息量是多少?
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