#35 Var(X + Y) = Var(X)+Var(Y)+2Cov(X,Y) proof

[@gautamsethi3751]

Nice proof but in the end you assume that correlation is defined only for linear relationships. While the Pearson expression captures only linear correlation, in general there are many other measures of correlation, some of which measure the strength of non-linear relationships. Thus, it *is* correct that to say that no correlation and independence are synonymous; what you need to say is that the independence implies zero *linear* correlation but zero *linear* correlation does not imply independence.

[@yasminyasmin9591]

thank you so much. it's really helpful.

[@indernesgud6457]

Very Helpful! Good job brother

[@adrianag.5954]

Pretty good video, easy to understand!

[@AthoMIcroN]

Question : what gives you the right to "distribute" the expectation operation to each term ?

[@GarrettPetersen]

You can do that so long as the terms are linear.

[@gautamsethi3751]

By *the right* do you mean why can one *distribute* the expectations operator? It's simply because the expectations operator is linear: E(X) = p1X1+p2X2+...+pnXn, which allows one can factor out or distribute terms.

[@gautamsethi3751]

It's not that the *terms* are linear - it's because the operator *itself* is linear.

[@deborahfranza2925]

BLESS YOU THANK YOU SO MUCH

[@ugkim1111]

Thank you very much!!!! MERCI!!!!!

[@hauras6583]

Missing a bracket at the end there, bro 2:20. Safe for the vid.

[@tougue]

and quite a few other ones around the squares

[@prashant0104]

thank you so much!

[@ngocphuong3352]

thanks so much ^^~

[@duncancheruiyot8195]

Kindly guys if someone can proof for me var x =E(x^2)-(E(x))^2 but not the one given on this video that var x =E(x-E(x))^2

[@PhilChanstats]

Perhaps you are asking for this proof: kzbin.info/www/bejne/aYC9mGCnfdR0q5o

[@benjaminmichael2007]

thank you

[@kashbaywc]

lots of help thank you

[@gghsstiruttani8291]

thanks

[@ziranyang1238]

good job

[@jakabbaZ]

Kiits avust.

[@doudoulebrun1525]

Thank you for the help, but please watch your mouth, you make weird noises all video long. Thank you