Mathematics in Research

This Blog is Mainly for those who are doing Full Fledged Research in Wireless Communications and Signal Processing,Control Systems, Power Systems, Chemical Engg,Computer Science,etc .Math Prequisites for this include Calculus, Differential Equations,Probability and Stochastic Process,Signal Analysis,Linear Algebra,Optimization,Real and Complex Analysis, Information Theory and List Goes on...I will be Posting some Interesting Problems in these Math Fields and Discussions are Most Welcomed :)

Thursday, 26 April 2012

Independence and UnCorrelated

We Know that if Two Random variables

$X$ and

$Y$ are Independent Statistically, Then

$E(XY)=E(X)E(Y)$ , i.e., They are UnCorrelated. It Doesnt Mean that Dependent Random Variables are Always Correlated. Lets Think of Some Examples with Dependent Random Variables being UnCorrelated.

1 comment:

ekaveera26 April 2012 at 05:48
Let $X$ be any Random Variable with pdf having Even Symmetry i.e.,

$f_X(-x)=f_X(x)$ , Then
$E(X^{2k+1})=0, \forall k \in \mathbb Z_{\ge 0}$
Now if random variable $Y=X^{2k} \forall k \in \mathbb Z_{\ge 0}$ ,i.e., $Y$ is Dependent on $X$ , Then

$E(XY)=0$ From above. Also $E(X)=0$ for $k=0$ , so $E(X)E(Y)=0$

so $E(XY)=E(X)E(Y)$
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Thursday, 26 April 2012

Independence and UnCorrelated

1 comment: