deletions | additions       diff --git a/Waveform optimization.tex b/Waveform optimization.tex  index 0609ea9..86a3b63 100644  --- a/Waveform optimization.tex  +++ b/Waveform optimization.tex 
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We can now expand the integral:  $\idotsint \prod_j^N \prod_u^{N_j} dx_j^u dx_u^j  \sum_i^N [ \sum_t^{T_i} (d_t^i - m(x_t^i))^2 ]P(X|D,\Theta_{k-1})$ $ = \sum_i^N \sum_t^{T_i} \idotsint \prod_j^N \prod_u^{N_j} dx_j^u dx_u^j  (d_t^i - m(x_t^i))^2 P(X|D,\Theta_{k-1})$ $ = \sum_i^N \sum_t^{T_i} \iint dx_i^t dx_t^i  (d_t^i - m(x_t^i))^2 \idotsint \prod_{j\neq i}^N \prod_{u\neq t}^{N_j} dx_j^u dx_u^j  P(X|D,\Theta_{k-1})$ $ = \sum_i^N \sum_t^{T_i} \iint dx_i^t dx_t^i  (d_t^i - m(x_t^i))^2 P(x_t^i|D,\Theta)$