All Questions
Tagged with conditional-independence conditional-expectation
6
questions
1
vote
1
answer
106
views
Conditional expectation function and causal inference
!For the question itself skip to the last paragraph!
It is my understanding that iff we have a model of the form $$Y = m(X) + e$$ and $E[e|X] = 0$ we know that $m(X)$ is the conditional expectation ...
- 265
2
votes
0
answers
81
views
Ratio between expectation of maximum of $n$ and $n-1$ IID random variables
Let $X_1, ..., X_n$ be iid random variables. Define $Z_n = \max(X_1, ..., X_n)$. Can we lower bound
$$\mathbb{E}[Z_{n-1}] \geq (1-f(n))\mathbb{E}[Z_n]$$
Using some $f(n)$. I am mainly interested in ...
- 253
9
votes
3
answers
948
views
If $X$ and $Y$ are uncorrelated random variables, then under what condition is $E[X \mid Y] \approx E[X]?$
Suppose $X$ and $Y$ are real random variables that are uncorrelated. Now, uncorrelated does not imply independence, so $E[X \mid Y] \ne E[X]$.
However, can they be said to be approximately equal? If ...
- 3,454
4
votes
1
answer
449
views
Variance of the product of two conditional independent variables
Now I know that the variance of the product of two independent variables $Y$ and $Z$ is:$\DeclareMathOperator{\Var}{Var}$
$\Var(YZ) = \Var(Y)\Var(Z) + \Var(Y)E(Z)^2+\Var(Z)E(Y)^2$
However I would like ...
- 257
4
votes
1
answer
163
views
Computing probability distributions in the two envelope problem
I am trying to understand the resolution to the two envelope problem. While I am still working my way through it and so far the progress has been good I am stuck at a claim that one of the sources ...
- 2,603
2
votes
1
answer
150
views
Independence and conditional distribution
In a problem that I'm solving I find that:
"Let data (yi,xi) be sampled randomly from a two-dimensional distribution such that y|x is N(ɑ,x^2σ^2)".
Are y and x i.i.d? maybe just identically ...
- 55