consider a discrete memory less source with source s= { S0,S1,S2,S3} with probabilities P0=1/8 , P1= 1/8, P2=1/2 , P3=1/4
prove that h(s^3)=3h(s) using C++ program ?
I try this but not true
# include <iostream>
# include <cmath>
using namespace std;
int main()
{
float S0,S1,S2,S3;
float Hs,Hs3;
float X_1,X_2,X_3,X_4,X_5,X_6,X_7,X_8,X_9,X_10,X_11,X_12,X_13,X_14,X_15,X_16;
cout<<"Enter the first probability value : "<<endl;
cin>>S0;
cout<<"Enter the second probability value : "<<endl;
cin>>S1;
cout<<"Enter the third probability value : "<<endl;
cin>>S2;
cout<<"Enter the fourth probability value : "<<endl;
cin>>S3;
X_1=(S0*S0)*3.32*log10(1/(S0*S0));
X_2=(S0*S1)*3.32*log10(1/(S0*S1));
X_3=(S0*S2)*3.32*log10(1/(S0*S2));
X_4=(S0*S3)*3.32*log10(1/(S0*S3));
X_5=(S1*S0)*3.32*log10(1/(S1*S0));
X_6=(S1*S1)*3.32*log10(1/(S1*S1));
X_7=(S1*S2)*3.32*log10(1/(S1*S2));
X_8=(S1*S3)*3.32*log10(1/(S1*S3));
X_9=(S2*S0)*3.32*log10(1/(S2*S0));
X_10=(S2*S1)*3.32*log10(1/(S2*S1));
X_11=(S2*S2)*3.32*log10(1/(S2*S2));
X_12=(S2*S3)*3.32*log10(1/(S2*S3));
X_13=(S3*S0)*3.32*log10(1/(S3*S0));
X_14=(S3*S1)*3.32*log10(1/(S3*S1));
X_15=(S3*S2)*3.32*log10(1/(S3*S2));
X_16=(S3*S3)*3.32*log10(1/(S3*S3));
Hs = S0*3.32*log10(1/S0)+S1*3.32*log10(1/S1)+S2*3.32*log10(1/S2)+S3*3.32*log10(1/S3);
Hs3=X_1+X_2+X_3+X_4+X_5+X_6+X_7+X_8+X_9+X_10+X_11+X_12+X_13+X_14+X_15+X_16;
cout<<"The Entropy of entered probability is : "<<Hs<<endl;
cout<<"The Entropy of entered probability is : "<<Hs3<<endl;
cout<<endl;
system ("pause");
return 0;
}

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