QUESTION: Normal Distribution

yojo101

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Jan 28, 2010, 2:46:37 PM1/28/10

to KV CFA L1 June 2010

Please explain to me the statement "A linear combination of normally
distributed variables is also normally distributed".

Dhruv Lilaramani

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Jan 28, 2010, 3:27:29 PM1/28/10

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If X₁, X₂ are two normal random variables, with means μ₁, μ₂ and standard deviations σ₁, σ₂, then their linear combination will also be normally distributed.

$aX_1 + bX_2 \ \sim\ \mathcal{N}(a\mu_1+b\mu_2,\, a^2\!\sigma_1^2 + b^2\sigma_2^2)$

On Fri, Jan 29, 2010 at 1:16 AM, yojo101 <yoj...@gmail.com> wrote:

Please explain to me the statement "A linear combination of normally
distributed variables is also normally distributed".

--
The best way to deliver a punch is to step back, but step back a little too much, and you ain't fighting at all.

Nikhil Gupta

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Jan 28, 2010, 11:30:01 PM1/28/10

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Hi,

A linear combination of two variables is nothing but the equations we all know i.e. like aX+bY = ….

Where X, Y are variables and a,b are constants

Therefore the statement "A linear combination of normally distributed variables is also normally distributed"

States that that if X, Y variables are normally distributed then the equations like above(which are noting but the linear comb of X,Y) are also normally distributed or in other words if you plot the graph of aX+bY then that also will be like normally bell shaped as the graph of X and Y.

Regards,

Nikhil Gupta

From: Dhruv Lilaramani [mailto:dhruv.li...@gmail.com]
Sent: Friday, January 29, 2010 1:57 AM
To: kv-cfa-l1...@googlegroups.com
Subject: Re: QUESTION: Normal Distribution

If X₁, X₂ are two normal random variables, with means οΏ½₁, οΏ½₂ and standard deviations οΏ½₁, οΏ½₂, then their linear combination will also be normally distributed.

$Image removed by sender. aX_1 + bX_2 \ \sim\ \mathcal{N}(a\mu_1+b\mu_2,\, a^2\!\sigma_1^2 + b^2\sigma_2^2)$

yojo101

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Feb 13, 2010, 3:10:26 AM2/13/10

to KV CFA L1 June 2010

Thank you guys

On Jan 29, 9:30 am, Nikhil Gupta <nikhil.g.gu...@oracle.com> wrote:
> Hi,
>
>
>

> A linear combination of two variables is nothing but the equations we all know i.e. like aX+bY = ..

>
> Where X, Y are variables and a,b are constants
>
>
>
> Therefore the statement "A linear combination of normally distributed variables is also normally distributed"
>
> States that that if X, Y variables are normally distributed then the equations like above(which are noting but the linear comb of X,Y) are also normally distributed or in other words if you plot the graph of aX+bY then that also will be like normally bell shaped as the graph of X and Y.
>
>
>
> Regards,
>
> Nikhil Gupta
>
>
>
> From: Dhruv Lilaramani [mailto:dhruv.lilaram...@gmail.com]
> Sent: Friday, January 29, 2010 1:57 AM
> To: kv-cfa-l1...@googlegroups.com
> Subject: Re: QUESTION: Normal Distribution
>
>
>

> If X1, X2 are two normal random variables, with means μ1, μ2 and standard deviations σ1, σ2, then their linear combination will also be normally distributed.

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