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Results tagged with variance
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user 81598
The expected squared deviation of a random variable from its mean; or, the average squared deviation of data about their mean.
1
vote
1
answer
119
views
What is my missing assumption is sum of variances?
In this answer, it says that in general the sum of the variances is not equal to the variance of the sum. … I tried to work it out by myself, and I think I got a different result, namely that the variance of the sum is equal to the sum of the variances. …
- 1,719
20
votes
5
answers
43k
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Variance of linear combinations of correlated random variables
I understand the proof that
$$Var(aX+bY) = a^2Var(X) +b^2Var(Y) + 2abCov(X,Y), $$
but I don't understand how to prove the generalization to arbitrary linear combinations.
Let $a_i$ be scalars for $i\i …
- 1,719
3
votes
1
answer
1k
views
Variance of $a^TX$ for MVN X
How do you show that the variance of $a^TX$ for multivariate normal X is $a^T\Sigma a$?
I have $V(a'X)=E(a'X-E[a'X])^2$, but it seems like the dimensions get messed up or something after that. …
- 1,719
5
votes
2
answers
1k
views
Does rounding introduce variance into estimates?
Does rounding introduce variance to the parameter estimate, however? Seems like it's just adding a stochastic component, which would introduce variance. … How much variance does rounding introduce?
If rounding does introduce variance, how do we know when it's worth that cost? …
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