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].

27 мая 2019 г. · By the expression E(XY), we mean the expectation of XY under their joint distribution. I.e., if these both are continuous, we have that.

11 июн. 2021 г. · The law of total expectations states E[xy]=E[E[xy|x]]. By linearity of conditional expectations, E[E[xy|x]]=E[xE[y|x]].

10 окт. 2014 г. · The difference between E(X∣Y) and E(X∣Y=y) is that the former is a random variable, whereas the latter is (in some sense) a realization of E(X∣Y).

25 авг. 2014 г. · Suppose I have two independent normal variables X and Y with known mean and variance. Defining Z=X+Y, what is the most straightforward way to compute E[X|Z]?

12 дек. 2019 г. · The conditional expectation E(Y|X=x) is a function g(x) of x. For a fixed value x this is not a random variable.

17 сент. 2017 г. · E(X|Y) is a random variable, defined for all outcomes of Y, that is equal to the expectation of X given this outcome of Y (E(X|Y=a)).

8 июл. 2022 г. · When X and Y are independent, 0≠E(XY)=E(X)E(Y) implies E(X)≠0≠E(Y). Your conclusion will hold if and only if E[g(Y) ...

19 сент. 2022 г. · You can compute an expectation by summing over all possibilities. E[f(X,Y)|give some condition]=∑for all cases of x,yf(x,y)⋅p(X=x,Y=y).

20 сент. 2015 г. · The conditional density function g(y|x) depends on both y and x but then you integrate yg(y|x) over y when taking the expectation. – Neznajka.