Some basic things in Probability

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SherlockBenedict

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I want to summarize certain things in probability that are useful for communication. I would just like to know if they are correct-

Var(a+b) = Var(a) + Var(b) + 2 R(ab) where R() indicates correlation


given that two Z= X+ Y


mean square value of Z= Mean square value of (X + Y)

and

mean square value of Z = Mean square value of X + Mean square value of Y if X and Y are uncorrelated





Are these correct?
 
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Everything is correct except that

\[var(a+b) = var(a) + var(b) + 2*covar(a,b)\].

The correlation between a and b is defined as
\[R(a,b) = \frac{covar(a,b)}{\sqrt{var(a)var(b)}\].
 

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