Xmaxima output : (%i20) foo(x,mu,sigma):=(1/(sigma*sqrt(2*%pi)))*exp(-((x-mu)^2)/(2*sigma^2)); 2 1 - (x - MU) (%o20) foo(x, MU, SIGMA) := ----------------- EXP(-----------) SIGMA SQRT(2 %PI) 2 2 SIGMA (%i21) bar(x,m1,s1,m2,s2):=defint(foo(t,m1,s1)*foo(x-t,m2,s2),t,minf,inf); (%o21) bar(x, m1, s1, m2, s2) := DEFINT(foo(t, m1, s1) foo(x - t, m2, s2), t, MINF, INF) (%i22) assume(sigma[1]>0,sigma[2]>0); (%o22) [REDUNDANT, REDUNDANT] (%i23) bar(x,mu[1],sigma[1],mu[2],sigma[2]); 2 2 2 x + (- 2 MU - 2 MU ) x + MU + 2 MU MU + MU 2 1 2 1 2 1 - ------------------------------------------------ 2 2 2 SIGMA + 2 SIGMA 2 1 SQRT(2) %E (%o23) ------------------------------------------------------------ 2 2 2 SQRT(%PI) SQRT(SIGMA + SIGMA ) 2 1 (%i24) forget(sigma[1]>0,sigma[2]>0); (%o24) [SIGMA > 0, SIGMA > 0] 1 2 (%i25) bar(x,mu[1],sigma[1],mu[2],sigma[2]); Is SIGMA positive or negative? 1 pos;Is SIGMA positive or negative? 2 pos; 2 2 2 x + (- 2 MU - 2 MU ) x + MU + 2 MU MU + MU 2 1 2 1 2 1 - ------------------------------------------------ 2 2 2 SIGMA + 2 SIGMA 2 1 SQRT(2) %E (%o25) ------------------------------------------------------------ 2 2 2 SQRT(%PI) SQRT(SIGMA + SIGMA ) 2 1 (%i26)