I need to confirm Professor's error

[Dari]

We're reviewing statistics problems and one is a generic integration problem:

Int(0, inf, y*exp(-k*y), dy)

Using Integration by parts, I get: 1/k^2

In his notes, he's getting: 1/k

Who's right?

 

[FoBoT]

http://www.pics.bbzzdd.com/bet...uaryTm/GoatPancake.jpg

 

[imported_yovonbishop]

I believe he's right. I think I remember a rule from stats where if you've got the integration of y*exp(-y) your answer is 1 (which is actually 1/1). So if you've got a k in front, it's going to be 1/k or whatever that variable is.

If I'm wrong, it just goes to show that I didn't learn anything in statistics. Good luck though.

 

[Dari]

Originally posted by: yovonbishop
I believe he's right. I think I remember a rule from stats where if you've got the integration of y*exp(-y) your answer is 1 (which is actually 1/1). So if you've got a k in front, it's going to be 1/k or whatever that variable is.

If I'm wrong, it just goes to show that I didn't learn anything in statistics. Good luck though.

This is a math problem, not statistics.

 

[darkxshade]

Originally posted by: Dari

Originally posted by: yovonbishop
I believe he's right. I think I remember a rule from stats where if you've got the integration of y*exp(-y) your answer is 1 (which is actually 1/1). So if you've got a k in front, it's going to be 1/k or whatever that variable is.

If I'm wrong, it just goes to show that I didn't learn anything in statistics. Good luck though.

This is a math problem, not statistics.

This is a communication problem(you think you're right, the professor does not), not math

 

[Tiamat]

The answer is 1/k²

This tool is very convenient for integration when you don't want to do it by hand and do not have a mathcad/matlab/maple software readily available.

Solve the integral in its indefinite form first, then apply the boundary conditions. The first term drops because exp (-inf) is zero. The second term because -1/k². Since the second term is subtracted from the first, the overall solution is 1/k².

Either the question is wrong, our your professor made a mistake.

 

[ViviTheMage]

Originally posted by: Tiamat
The answer is 1/k²

This tool is very convenient for integration when you don't want to do it by hand and do not have a mathcad/matlab/maple software readily available.

Either the question is wrong, our your professor made a mistake.

So, dari is correct?

 

[Tiamat]

Originally posted by: ViviTheMage

Originally posted by: Tiamat
The answer is 1/k²

This tool is very convenient for integration when you don't want to do it by hand and do not have a mathcad/matlab/maple software readily available.

Either the question is wrong, our your professor made a mistake.

So, dari is correct?

Since dari obtained 1/k² from integration by parts, he is correct. Mathematical tools also agree with dari's solution. I am too lazy to do the IBP right now as a 3rd source of support.

This assumes that the question was written down correctly.

 

[Dari]

Originally posted by: Tiamat
The answer is 1/k²

This tool is very convenient for integration when you don't want to do it by hand and do not have a mathcad/matlab/maple software readily available.

Solve the integral in its indefinite form first, then apply the boundary conditions. The first term drops because exp (-inf) is zero. The second term because -1/k². Since the second term is subtracted from the first, the overall solution is 1/k².

Either the question is wrong, our your professor made a mistake.

Thank's. Since that simple example was used to show that using the Pareto distribution is easier than doing it my way, I think he's just missing a k somewhere. But I hate it when teachers make mistakes. I hate fixing peoples' mistakes.

BTW, a Pareto distribution is much better for modelling stock price behavior than the widely used lognormal distribution. I don't know why most people use the latter.

 

[jjones]

Originally posted by: FoBoT
http://www.pics.bbzzdd.com/bet...uaryTm/GoatPancake.jpg

I concur.