**Due**: June 7, 2017

**Points**: 30

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*30 points*) In Section 18.3.2.3, the formula*I*(*A*;*X*) =*p*(1 −*q*)^{n}+*p*[1 − (1 −*q*)^{n}] lg [1 − (1 −*q*)^{n}] − [1 −*p*(1 −*q*)^{n}] lg [1 −*p*(1 −*q*)^{n}]is derived. Prove that

*I*(*A*;*X*) is a maximum with respect to*p*when*p*=*M*/(*Mm*+ 1), with*M*and*m*as defined in that section.

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