\nonumber\\ &\times f_{\xi(i)|w(i-0)=m}(\xi(i)|w(i-0)=m)d\xi(i)\label{eq:constant_transmission_rate_0}\\ =&\sum_{m=0}^{\infty}\pi_{m}\int_{0}^{\infty}g(p_{c}(i))\Pr\left\{g(p_{c}(i))\leq \mathcal{I}(i)\right\}f_{\xi(i)|w(i-0)=m}(\xi(i)|w(i-0)=m)d\xi(i)\\ =&\sum_{m=0}^{\infty}\pi_{m}\int_{0}^{p}g(\xi(i))\Pr\left\{