Sentence examples for taking expectation from inspiring English sources

By taking expectation of packet reception and loss cases in the first product in (9), we can simplify expression (9) as: (10).

Integrating both sides for the above inequality from 0 to (tau_{varepsilon}wedge T) and taking expectation, we obtain EVbigl(S tau_{varepsilon}wedge T),x tau_{varepsilon}wedge T bigr)leq V(S_{0},x_{0})+C_{2}T.

Indeed, two key challenges encountered in the analysis of ergodic capacity include obtaining the exact PDF of the end-to-end SIR and taking expectation of the nonlinear log function.

Taking expectation to both sides of (78), we get the mean function of dynamic contact forces, m P m_{{P_{i} }} (t) = E[P_{i} (t)] = k_{i} E[Z_{i} (t)] + c_{i} E[dot{Z}_{i} (t)] = 0. (79) Open image in new window Fig. 9 A sketch of theith tire on rough pavement surface.

Now, taking expectation on both sides of the above equation and by employing Assumptions 1 and 2 will result in: textbf{E}[boldsymbol{tilde{x}}[k]] = (textbf{I} - mu textbf{G}textbf{C}^{T}[k]textbf{C}[k] textbf{A}[k-1]textbf{E}[boldsymbol{tilde{x}}[k-1]] (24).

Substituting the expression for a posteriori error from (26) in (30) and taking expectation on both sides to obtain the following relation: E [ ‖ v n + 1 ‖ A 2 ] = E [ ‖ v n ‖ A 2 ] − 2 μ E [ e a n A f ( e n ) ] + μ 2 E [ ‖ x n ‖ A 2 f 2 ( e n ) ]. (31).

Taking expectations on both sides, we get (D10).

By multiplying both sides of (12) by and taking expectations, we obtain (13).

Taking expectations on both sides of (3.11) and noticing that (3.16).

Assuming equiprobable symbols and taking expectations on both sides yields: E{hat{omega}_{i}(t)} = omega_{c}.

In particular, the following two difference equations, which are obtained by just taking expectations on both sides of Eqs.