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+//Page Number: 6.18

+//Example 6.14

+clc;

+//Given

+p=0.1;

+q=0.2;

+Pm0=0.5;

+Pr1bym0=p;

+Pr0bym1=q;

+

+//(a) Find Pr0 and Pr1

+

+Pm1=1-Pm0;

+Pr0bym0=1-Pr1bym0;

+Pr1bym1=1-Pr0bym1;

+

+//By formula

+//P(r0)=(P(r0/m0)*P(m0))+(P(r0/m1)*P(m1);

+//P(r1)=(P(r1/m0)*P(m0))+(P(r1/m1)*P(m1);

+

+Pr0=(Pr0bym0*Pm0)+(Pr0bym1*Pm1);

+Pr1=(Pr1bym0*Pm0)+(Pr1bym1*Pm1);

+disp(Pr0,'P(r0):');

+disp(Pr1,'P(r1):');

+

+//(b)P(m0/r0)

+//Using Bayes Rule

+//P(m0/r0)=(P(m0)*P(r0/m0)/P(r0))

+Pm0byr0=(Pm0*Pr0bym0)/Pr0;

+disp(Pm0byr0,'P(m0/r0):');

+

+//(c)P(m1/r1)

+//Using Bayes Rule

+//P(m1/r1)=(P(m1)*P(r1/m1)/P(r1))

+Pm1byr1=(Pm1*Pr1bym1)/Pr1;

+disp(Pm1byr1,'P(m1/r1):');

+

+//(d)Probabilty error

+//As Pe=(P(r1/m0)*P(m0))+(P(r0/m1)*P(m1))

+Pe=(Pr1bym0*Pm0)+(Pr0bym1*Pm1);

+disp(Pe,'Probability error:');

+

+//(e)Probabilty that is transmitted correctly

+//As Pc=(P(r0/m0)*P(m0))+(Pr1bym1*Pm1)

+

+Pc=(Pr0bym0*Pm0)+(Pr1bym1*Pm1);

+disp(Pc,'Probabilty that is transmitted correctly:');

+

+