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.
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.
Let X be any Random Variable with pdf having Even Symmetry i.e.,
ReplyDeletefX(−x)=fX(x), Then
E(X2k+1)=0,∀k∈Z≥0
Now if random variable Y=X2k∀k∈Z≥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)