I checked Histogram in Wiki, where there is also some inaccuracy: "The total area of a histogram always equals 1". This is true ony if we define the width of bin as unit interval. But visually/conceptually(?), this width is not one. It corresponds to the real meaning/definition of the horizon axis. This leads to the discrepency in this post and most discrete cases.

I checked Histogram in Wiki, where there is also some inaccuracy: "The total area of a histogram always equals 1". This is true ony if we define the width of bin as unit interval. But visually/conceptually(?), this width is not one. It corresponds to the real meaning/definition of the horizon axis. This leads to the discrepency in this post and most discrete cases.

Thanks, Alec. To show this proposal, we need E(x)<infinity. Is it enough? Is there a way Maple can establish and understand this assumption well? In addition, I am always uncertain if "assume(y<infinity)" is a correct way to establish an upper bounded real variable in Maple.

You guys' discussion on continuity assumption is also quite helpful.

Thanks, Alec. To show this proposal, we need E(x)<infinity. Is it enough? Is there a way Maple can establish and understand this assumption well? In addition, I am always uncertain if "assume(y<infinity)" is a correct way to establish an upper bounded real variable in Maple.

You guys' discussion on continuity assumption is also quite helpful.

Are you saying your Maple returns infinity. But It works on mine to return one. I am using v11.02.

Now Maple can show the intitial proposal raised in the beginning.

with(Statistics):
rv:=RandomVariable(Normal(mu,sigma)):
Fc:=1-CDF(rv,x):
limit(Fc*x,x=infinity,left) assuming sigma>=0;

It works. It seems we should avoid global assumptions like "real", thanks to Axel Vogt's reply in this discussion.

Jakubi: The paper you recommended opens the door for me to the core issue. Thanks.

Are you saying your Maple returns infinity. But It works on mine to return one. I am using v11.02.

Now Maple can show the intitial proposal raised in the beginning.

with(Statistics):
rv:=RandomVariable(Normal(mu,sigma)):
Fc:=1-CDF(rv,x):
limit(Fc*x,x=infinity,left) assuming sigma>=0;

It works. It seems we should avoid global assumptions like "real", thanks to Axel Vogt's reply in this discussion.

Jakubi: The paper you recommended opens the door for me to the core issue. Thanks.