ns know that $\operatornameVar=\operatornameCov=a^2\operatornameVar+2ab\operatornameCov+b^2\operatornameVar$ (by broadening $(ax+by)(ax+by)$ and lettinns $\operatornameVar=x^2$-terms, $\operatornameVar=y^2$-state and $\operatornameCov=xy$-terms).

You are watching: Var(ax+by)

but what happens when we"ve gained a $x$-hatchet or a $y-$hatchet top top its own?

e.g. Say we desire $\operatornameVar$.

then us have $(x+y+1)^2=x^2+2xy+2x+y^2+2y+1$, so:$$\operatornameVar=\operatornameVar+2\operatornameCov+2?+\operatornameVar+2?+1.$$ can someone fill in ns blanks?

Thanks.


probcapability statisticns random-variables
Shto be
mention
Follow
edited may 21 "14 in ~ 16:12
*

Hakns
9,57377 yellow badges3737 silver- badges5757 copper badges
request may 21 "14 at 16:09
*

beep-boopbeep-boop
11k1010 gold badges4040 silver badges6868 copper title
$\endgroup$
2
include a commenns |

2 Answers 2


energetic oldest Votes
1
$\begingroup$
girlfriend almost acquired it other than the $$\textCov(aX, bY+c) = \textCov(aX, bY)+\textCov(aX,c) = Abdominal \textCov(X,Y) +0$$Since covariance of a arbitrarily variable through a consistent ins $0$.

http://www.kaspercpa.com/statisticalreview.htm


Share
cite
Folshort
answered might 21 "14 in ~ 16:17
*

AlexAlex
18.5k44 gold badges2424 silver- badges3838 bronze badges
$\endgroup$
5
add a comment |
1
$\begingroup$
If all friend desire ins the variance, getting it via the covariance recipe the means you"re doinns ins a lons even more complex 보다 it needs come be. Friend simply observe: $$\rm Var = \rm Var,$$ Because $\rm Var = \rm Var$ for any consistent $c$. Then girlfriend have the right to usage the covariance formula.


Share
mention
Follow
answered might 21 "14 at 16:25

heropupheropuns
103k1212 gold badges8383 silver- badges144144 bronze title
$\endgroup$
3
add a comment |

your price


thanks for contributinns a response come startupcuba.orgematicns ridge Exchange!

please be sure come prize ns question. Administer detailns and shto be her research!

but avoid

asking because that help, clarification, or respondinns to other answers.Makinns statementns based on opinion; earlier them up through referrals or personal experience.

usage startupcuba.orgJax come Style equations. Startupcuba.orgJax reference.

come Discover more, watch our advice ~ above composing good answers.

See more: Has Anyone Ever Been So Far As, View Question 


draft saved
breeze discarded

sign uns or log in


sign up using Google
authorize up utilizing FaceBook
authorize up using email and Pasknife
submit

post together a guest


name
email Required, yet never shown


post together a guest


name
email

Required, however never before shown


short article your answer Dismap

through click “post her Answer”, you agree come our terms of service, privacy policy and cookie policy


no ns price you're lookinns for? browse other inquiries tagged probcapability statistics random-variables or ask her very own question.


ns Overflow Blog
Featured top top Meta
related
2
E(XY) expectati~ above product
3
how come compute variance that a conditionatogether expectati~ above and also vice versa
1
how to uncover the variance that $U= X-2Y+4Z$? & ns Co-variance the $U=X-2Y+4Z$ and $V = 3X-Y-Z$
0
recognize ns worths the $a$ and $b$ therefore the $Var(Q)$ ins at minimum
0
show the $\operatornameVarS^2=\frac1n(Е(X_i-EX_i)^4 - \fracn-3n-1\sigma^4)$
1
exactly how come construct a Cross-associated Covariance matrix by resolving one equation with Covariance and Variance expressitop top the a unwell-known random variable?
hot Netoccupational concerns more hot concerns

Inquiry feed
subscribe come RSs
Concern feed to subscribe to thins RSs feed, copy and paste this URtogether right into her RSns reader.



startupcuba.orgematics
firm
ridge Exreadjust Network
site design / logo design © 2021 ridge Exchange Inc; user contributions a license is granted under cc by-sa. Rev2021.10.1.40358


startupcuba.orgematicns ridge Exchange works best through Javascript enabled
*

your privacy

through clicking “accept all cookies”, girlfriend agree ridge Exadjust can keep cookie ~ above her tool and disclose information in accordance through our Cookie Policy.