27 мар. 2019 г. · This is correct: E[XY]=E[E[XY|X]]=E[X[E[Y|X]]=E[X(a+bX)]. By linearity of the expectation operator, we get E[XY]=aE[X]+bE[X2]. Conditional expectation of $X$ given $Z = X + Y - Cross Validated E(XY)=E(XE(Y|X) Joint Conditional Expectations [duplicate] Conditional Expectation : How is E[E[xy|x]]=E[xE[y|x]]? Другие результаты с сайта stats.stackexchange.com

Conditional expectations such as E[X|Y = 2] or E[X|Y = 5] are numbers. If we consider E[X|Y = y], it is a number that depends on y. So it is a function of y.

Conditional expectation, E(X |Y ), is a random variable with randomness inherited from Y , not X. Example: Suppose Y = 1 with probability 1/8,. 2 with ...

Hence, E(XY|Y)=. YE(X|Y) by the definition of the conditional expectation. 2. Corollary. E(XY) = E[YE(X|Y)]. Proof. E(XY) = E[E(XY|Y)] = E[YE(X|Y)]. 2.

In probability theory, the conditional expectation, conditional expected value, or conditional mean of a random variable is its expected value evaluated

24 апр. 2024 г. · I would like to show or see a proof that the conditional expected value E[X|Y] is a function of Y for arbitrary random variables X,Y (especially not discrete ...

As with the variance, Cov(X, Y ) = E(XY ) - (EX)(EY ). It follows that if X and Y are independent, then E(XY )=(EX)(EY ), and then Cov(X, Y )=0.

Remember that the conditional expectation of X given that Y=y is given by E[X|Y=y]=∑xi∈RXxiPX|Y(xi|y). Note that E[X| ...

E[Y ] = X y∈Y yp(y). • We can interpret E[Y |X = x] or E[Y | x] as the expectation of the condi- tional distribution of Y given X = x. If X is also a ...

For this theorem, the conditional expectation E(X|Y ) is the best esti- mate of X based on the observations of Y . Example 7.16 Assume that X = aY + ε, where a ...