In information theory (the mathematical study of communication systems, which figures prominently inelectrical engineering), the information (or entropy) of a discrete and finite random variable X is defined as:H(X)= E[log2(1/P(X))]where p(.) is the PMF for X. Answer the following:1. Assume that the set of values that X can take is {x1, ..., xn} and p(x;) > 0 for all i. Derive anexpression for H(X) in terms of p(x1), ..., p(xn).2. Assume that n = 2. What values of p(x1) and p(x2) maximize H(X)?

Name: In information theory (the mathematical study of communication system
Uploaded: 2024-03-20T07:06:41.000Z
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Description: In information theory (the mathematical study of communication systems, which figures prominently inelectrical engineering), the information (or entropy) of a discrete and finite random variable X is defined as:H(X)= E[log2(1/P(X))]where p(.) is the

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In information theory (the mathematical study of communication systems, which figures prominently in electrical engineering), the information (or entropy) of a discrete and finite random variable X is defined as: H(X) = E[log2(1/p(X))] %3D where p(.) is the PMF for X. Answer the following: 1. Assume that the set of values that X can take is {x1,.., xn} and p(x;i) > 0 for all i. Derive an expression for H(X) in terms of p(x1), ..., p(xn). 2. Assume that n = 2. What values of p(x1) and p(x2) maximize H(X)?