Question 2. (6 marks) ent ment ssment essment sessment Assessr Assessment T Assessment UT Assesment esse QUT Asses QUT A

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Question 2 6 Marks Ent Ment Ssment Essment Sessment Assessr Assessment T Assessment Ut Assesment Esse Qut Asses Qut A 1 (145.01 KiB) Viewed 22 times

Question 2. (6 marks) ent ment ssment essment sessment Assessr Assessment T Assessment UT Assesment esse QUT Asses QUT Ass Ind ent QUT Asse ment ssment sessment essment ssme ussas mer essme either 0 or 1) in A transmission system sends messages 8 bits (i.e., 8 digits that take values length. Transmitted messages are often corrupted by errors, whereby bits that were originally 0 are switched to 1 or vice versa (fig. 2). Original 01111001 0 1 0 1 1 1 0 1 Corrupted 0 1 0 1 1 1 0 1 0 1 1 1 1 1 0 1 X X X X = 2 X = 1 Figure 2: Two transmitted and corrupted messages with X = 2 and X = 1 errors, respectively. The total number of such errors present in a message is given by the discrete random variable sessm X with probability mass function Pr(X = x) = p(x) for x = {0, 1,..., 8} where p(x) is given by k, if x = 0, { 1 if x = {1,2,..., 8). x(x + 1)' (a) Find k such that p(x) is a valid probability mass function. (b) Calculate the standard deviation of X. Note that you may find the followingment QUI results 8 1 8 15551 4609 2520 and x+1 Σ x=1 x+1 2520 x=1 The entropy of a random variable represents the amount of information in the variable. For a discrete random variable the entropy is given by -E(ln(p(x))). Calculate the entropy X. smen ssessme sessmen queu p(x) = essment mei sment sessme smer me essm ssment. Ass Asses ssess sessm essi essme นอนว่ ment sse? sm essme Assess Asses smer sessmen sessment Ass essment ssment ment ssment ssment ssment S essment ssment ques ewss Assess ent QUT Asses ment sme essment