Year 12s: what will be the first way you research your future options? >>

correlation

ike222

please how do i calculate Corr(X+Y,X-Y)

Reply 1

RDKGames

Study Forum Helper

Original post by ike222

please how do i calculate Corr(X+Y,X-Y)

Ignore that last post if you saw it - I've misread Corr for Cov twice!

So then, denote

X+Y=Z

and

X-Y = W

hence we get that

Unparseable latex formula:

\begin{aligned} \mathrm{Corr}(Z,W) & = \dfrac{\mathrm{Cov(Z,W)}}{\sigma_Z \sigma_W} \\ & = \dfrac{\mathbb{E}[X^2-Y^2]-\mathbb{E}[X+Y] \cdot \mathbb{E}[X-Y]}{\sigma_{X+Y}\sigma_{X-Y}}

where

\sigma_{X+Y}

and

\sigma_{X-Y}

as the standard variation of the two distributions respectively.

(edited 5 years ago)

Reply 2

ike222

Original post by RDKGames

Ignore that last post if you saw it - I've misread Corr for Cov twice!

So then, denote

X+Y=Z

and

X-Y = W

hence we get that

Unparseable latex formula:

\begin{aligned} \mathrm{Corr}(Z,W) & = \dfrac{\mathrm{Cov(Z,W)}}{\sigma_Z \sigma_W} \\ & = \dfrac{\mathbb{E}[X^2-Y^2]-\mathbb{E}[X+Y] \cdot \mathbb{E}[X-Y]}{\sigma_{X+Y}\sigma_{X-Y}}

where

\sigma_{X+Y}

and

\sigma_{X-Y}

as the standard variation of the two distributions respectively.

Thank you very much

Quick Reply

Related discussions

Latest

Articles for you

Terms and conditions

The Student Room Group Privacy Notice

What is an LLM and how could it benefit your career?

Powerful questions business students forget to ask their career advisers