Classification of obesity

In probability theory, a random variable Y is said to be mean independent of random variable X if and only if E(Y|X) = E(Y) for all x such that ƒ₁(x) is not equal to zero. Y is said to be mean dependent if E(Y|X) ≠ μ(y) for some x such that ƒ₁(x) is not equal to zero.Template:Clarify

According to Template:Harvtxt and Template:Harvtxt, Stochastic independence implies mean independence, but the converse is not necessarily true.

Moreover, mean independence implies uncorrelation while the converse is not necessarily true.

The concept of mean independence is often used in econometrics to have a middle ground between the strong assumption of independent distributions $f_{X_1}\perp f_{X_2}$ and the weak assumption of uncorrelated variables $\text{Cov}(X_1,X_2)=0$ of a pair of random variables $X_1$ and $X_2$.

If X, Y are two different random variables such that X is mean independent of Y and Z=f(X), which means that Z is a function only of X, then Y and Z are mean independent.

References

• 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
  
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• 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
  
  My blog: http://www.primaboinca.com/view_profile.php?userid=5889534

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