X and Y are independent definition

X and Y are independent means “σ(X) and σ(Y ) are independent”.
Sample 1

Examples of X and Y are independent in a sentence

  • Equation (8) states that CMI2 is equal to CMI if the second and third terms of Equation (8) are zero,i.e. both X and Y are independent with Z.

  • If X and Y are independent of each other, the covariance Cov (X, Y ) is necessarily equal to zero, see Theorem 3.1. The converse is not true.

  • Let (X, Y ) be a 2-dimensional L´evy process such that Y is piece- wise constant and ∆Xt∆Yt = 0 for all t a.s. Then X and Y are independent.

  • Suppose X and Y are independent random variables of identical distribution such that X > 0 and E[X] < ∞.

  • The lower bound is achieved if X and Y are independent but the opposite does not hold: X and Y can be dependent and have their correlation equal to zero.

  • Recall that X and Y are independent if FX,Y (x, y) = FX (x)FY (y) for all x, y.

  • For example, if X and Y are independent, then knowing X does not give any information about Y and vice versa, so their mutual information is zero.

  • The third term is a covariance term which is negligible if X and Y are independent or uncorrelated.

  • Also, from inequality (5), we see that mutual information is non-negative and is 0 if and only if X and Y are independent.

  • Like mutual information, for a wide range of kernels HSIC(X, Y ) = 0 if and only if X and Y are independent [37], and large values of the measure correspond to “more dependence.” Unlike mutual information, HSIC incorporates a notion of ge-ometry (via the kernel choice), and is both statistically and computationally easy to estimate.

Related to X and Y are independent

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