I ask maxima to calculate a conditional average over a gaussian
distribution, the first time it asks questions and gives up, try it
again and it gives an answer...
(%i4) kill(all);
(%o0) done
(%i1) reset();
(%o1) [_, __, error, %, lispdisp, piece, labels, rhs, lhs]
(%i2) display2d:false;
(%o2) false
(%i3) pv:exp(-((vv-v1)/sqrt(T))^2/2)/sqrt(2*%pi*T);
(%o3) %e^-((vv-v1)^2/(2*T))/(sqrt(2)*sqrt(%pi)*sqrt(T))
(%i4) integrate(vv*pv,vv,-inf,0);
Is T positive or negative?
pos;
Is v1 positive, negative, or zero?
pos;
Is v1 positive, negative, or zero?
pos;
Is v1 positive, negative, or zero?
pos;
(%o4) ('integrate(vv*%e^-((vv-v1)^2/(2*T)),vv,-inf,0))/(sqrt(2)*sqrt(%pi)
*sqrt(T))
(%i5) pv:exp(-((vv-v1)/sqrt(T))^2/2)/sqrt(2*%pi*T);
(%o5) %e^-((vv-v1)^2/(2*T))/(sqrt(2)*sqrt(%pi)*sqrt(T))
(%i6) integrate(vv*pv,vv,-inf,0);
Is T positive or negative?
pos;
Is v1 positive, negative, or zero?
pos;
(%o6) -(gamma_incomplete(1,v1^2/(2*T))*T
-gamma_incomplete(1/2,v1^2/(2*T))*v1*sqrt(T)/sqrt(2))
/(sqrt(2)*sqrt(%pi)*sqrt(T))
(%i7)