Unformatted text preview: (a) What is EX ? (b) What is the minimum number of codewords that we need? (c) Provide good lower and upper bounds to the minimum expected length of a code for the values of X . 4. (a) Construct a Huﬀman code for the values of X speciﬁed in Problem 3. (b) What is the expected code word length for this code? 5. (a) Plot the entropy function H as a function of 0 ≤ p ≤ 1 when the random variable X has only two possible outcomes, the ﬁrst of which occurs with probability p . (b) For what value of p is the entropy H a maximum? 6. (a) Let the domain of a system S delay=1 consist of the functions { eα  t  : α ≥ } . What is the system response to an input with α = 0? What is the codomain of this system? (b) What is the codomain of the system S time=2 when the domain is given in (a)? 1...
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 Spring '06
 FINE
 Prefix code, binary tree representation, uniquely decodable code

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