Table 3. Summary of the derived expressions for confidence. In the interrogation condition expression L = 1 if R = 2 and L = -1 if R = 1. The free response expression applies for R = 2, while for R = 1 the integral limits change to −d_i+1 and −d_t. See Table 1 for further symbol definitions..

Condition	Expression for confidence
Interrogation	$\begin{array}{lll}p(C=i|R,E)\hfill & =\hfill & \frac{L}{\Phi \text{(}L\frac{{\mu }_{lp}}{{\sigma }_{lp}}\text{)}}[BvN(\frac{g}{\sqrt{1+h^2}},e_{i+1};\frac{-h}{\sqrt{1+h^2}})\hfill \\ \hfill & \hfill & -BvN(\frac{g}{\sqrt{1+h^2}},e_i;\frac{-h}{\sqrt{1+h^2}})].\hfill \end{array}$
	Where,
	$\begin{array}{lll}BvN(l_1,l_2,\rho )\hfill & =\hfill & {\displaystyle {\int }_{-\infty }^{l_1}{\displaystyle {\int }_{-\infty }^{l_2}\frac{1}{2\pi \sqrt{1-{\rho }^2}}{e}^{-\frac{1}{2(1-{\rho }^2)}(x^2+y^2-2xy\rho )}dxdy}}\hfill \\ g\hfill & =\hfill & \frac{L{\mu }_{lp}\sqrt{{\sigma }_m^2+{\sigma }_{lp}^2}}{{\sigma }_m{\sigma }_{lp}}\hfill \\ h\hfill & =\hfill & \frac{L{\sigma }_{lp}}{{\sigma }_m}\hfill \\ e_i\hfill & =\hfill & \frac{L{d}_i-{\mu }_{lp}}{\sqrt{{\sigma }_m^2+{\sigma }_{lp}^2}}\hfill \\ {\mu }_{lp}\hfill & =\hfill & \frac{E}{\theta (t_e)}\hfill \\ {\sigma }_{lp}^2\hfill & =\hfill & \frac{E^2{\sigma }_{\phi }^2+t_e{\sigma }_{occ}^2}{{\theta }^2(t_e)}\hfill \end{array}$
Free response	$p(C=i|R=2,t_r,E)={\displaystyle {\int }_{d_i}^{d_{i+1}}d{x}_{c}N(x_c;{\mu }_{lf},{\sigma }_{lf}^2+{\sigma }_m^2)}$
	Where,
	$\begin{array}{l}{\mu }_{lf}=\frac{1}{\theta (t_e)}(x_d+\text{Δ}E\frac{{\sigma }_{acc}^2+x_d{\sigma }_{\phi }^2\stackrel{-}{E}}{{\sigma }_{acc}^2+t_d{\sigma }_{\phi }^2{\stackrel{-}{E}}^2})\hfill \\ {\sigma }_{lf}^2=\frac{{\sigma }_{occ}^2}{{\theta }^2(t_e)}(\frac{\text{Δ}{E}^2{\sigma }_{\phi }^2}{{\sigma }_{occ}^2+t_d{\sigma }_{\phi }^2{\stackrel{-}{E}}^2}+I)\hfill \end{array}$