expectation of product of random variables inequality

Conditional expectation - Wikipedia Cauchy distribution. So suppose x, y are two non-independent random variables, given that I know the distribution of x p(x) and the distribution of y q(y), how can I find an upper bound on E[|x * y |] that is a function of p and q? Tchebychev's inequality asserts that if a random variable X has expected value „ †Tchebychev's inequality then, for each †>0, PfjX ¡„j>†g•var.X/=†2 The inequality becomes obvious if we define a new random variable Z that takes the value 1 when jX ¡„j>†, and 0 otherwise: clearly Z •jX¡„j2=†2, from which it follows . PDF Conditional Expectation and Martingales - University of Waterloo a dimensionless quantity obtained by dividing the covari-ance by the product of the standard deviations ofX andY. We develop an inequality for the expectation of a product of nrandom variables gener-alizing the recent work of Dedecker and Doukhan (2003) and the earlier results of Rio (1993). Deceptively simple inequality involving expectations of products of ... Deceptively simple inequality involving expectations of products of ... Note that this is Inequalities for deviations from expectation - Tufts University Taking expectation on both sides, it follows from the linearity of expectation, kX +Yk p 6 2p 1(kXk p + kYk p). On the expectation of operator norms of random matrices to a s-algebra, and 2) we view the conditional expectation itself as a random variable. if the expected number of descendants is 2, then we measure the actual number by . To motivate the de nition of the inner product given above, rst consider the case when the probability space is nite. 1.Introduction Let (Ω, ,P) be a probability space and let (X,Y) be a bivariate random vector defined on it. For k = 1 we get the expectation of X. Since Y 0, by Markov's inequality Pr(jX E(X)j ˙X) = Pr(Y 2E(Y)) 1 2: Intuitively, the probability of a random variable being k standard deviations from the mean is 1=k2. PDF Conditional Expectation - University of Texas at Austin You can always write max (x1,x2,x3) as max (x1,max (x2,x3)). So it is a function of y. Thus, the variance of two independent random variables is calculated as follows: Var (X + Y) = E [ (X + Y)2] - [E (X + Y)]2.

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