\(X\) is the number of bits in error in the next four bits transmitted. What is the expected value of the square of the number of bits in error? Now, \(h(X)=X^{2}\). Therefore,

\[ \begin{aligned} E[h(X)]= & 0^{2} \times 0.6561+1^{2} \times 0.2916+2^{2} \times 0.0486 \\ & +3^{2} \times 0.0036+4^{2} \times 0.0001=0.52 \end{aligned} \]