## 69 Reputation

19 years, 60 days

## Remark: definition of Histogram...

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.

## Remark: definition of Histogram...

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.

## You are right...

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.

## You are right...

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.

## avoid global assumptions...

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.

## avoid global assumptions...

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.

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