Dear friends. I'm working in derive 3.14 XM - perhaps an old vintage - but anyway. Perhaps someone can explain me why I couldn't get this done. The cexpected mean value of x if ln(x) is N(mu,sigma) is given below in line 2, but integrating that from 0 to inf doesn't lead to a good answer. Working it out by hand seems to be OK giving e^(mu+0.5*sigma^2).
x:epsilonReal (0, inf)
#e*(-0.5*((LN(x)-mu)/sigma)^2/SQRT(2*pi*sigma))
;Int(#2,x)
INT(#e*(-0.5*((LN(x)-mu)/sigma)^2/SQRT(2*pi*sigma)),x,0,inf)
;Simp(#3)
-inf*SIGN(sigma)^(3/2
)
Best wishes
Troels Ring, M.D
Department of Nephrology
Aalborg, Denmark
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