Let X be a standard normal random variable. Let Y be a continuous random variable such that

Question

fY|X(y|x)=1/√2π*exp(−(y+2x)^2/2).

Find E[Y|X=x] (as a function of x, in standard notation) and E[Y].
unanswered

Compute Cov(X,Y).
unanswered

Continuing from above, find the conditional expectation E[X∣Y=y] and conditional variance Var(X∣Y=y).

Hint: The conditional PDF of X given Y=y is of the form

h(y)exp(−g(x,y))

for some function h(y) and some quadratic function g(x,y). Rewriting the function g(x,y) in a familiar form will give E[X∣Y=y] and Var(X∣Y=y) without much computation.

E[X∣Y=y]= unanswered
Var(X∣Y=y)= unanswered

Answer 1

Does someone have the answer please?

Answer 2

No b/c you have to use your own knowledge first. It shows that you have a fixed mindset. If you don't believe me and the others, then you'll always be like that until you get a job

Answer 3

jiskha.com/questions/1798909/problem-4-gaussian-random-variables-let-x-be-a-standard-normal-random-variable-let-y-be

use this thread instead ^

Answer 4

-2x; 0; -2; -2y/5 and 1/5

Answer 5

I got 2y/5 for (4).