For every question related to the concept of conditional expectation of a random variable with respect to a $\sigma$-algebra. It should be used with the tag (probability-theory) or (probability), and other ones if needed.
Questions tagged [conditional-expectation]
4197 questions
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conditional expectation strange transformation
I have been given this question, but I don't get what to do.
I know I am supposed to condition on another variable, call it $Y$, which equals the number of flips until the first occurrence of…
Frank
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Conditional Expectation [Bak Sneppen Model]
I am reading the paper “Critical Threshols and the Limit Distribution in the Bak Sneppen Model” and I have difficulty proving the following statement:
The probability that at time $n$ we are in a block (b-avalanche) of range $k$ converges, as $n…
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Conditional expectation on the union of two events
Is there any property to simplify a conditional expectation of the form:
$\mathbb{E}[A| B\cup C]$
In my particular case, $A$ and $B$ are independent, so I would like to use the fact that $\mathbb{E}[A|B]=\mathbb{E}[A]$
Thank you
Juan Imbett
- 193
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Conditional expectations - E(X|X>5)
Struggling a little bit with this concept in class.
So using R I trialled 10,000 students taking a test (10 question, 4 multiple choice answers, only one of which is correct). I have a table of frequencies 0-10 how many correct answers each student…
kitkat1224
- 45
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Proving $L^1$ convergence of r.v. implies $L^1$ convergence of the conditional expectation
Let $X_n , X \in \mathcal L^1$ s.t. $X_n\rightarrow X $ in $\mathcal L^1$. Let $\mathcal g$ be a sub $\sigma$ algebra.
I want to show $$\mathbb E[X_n|\mathcal g] \rightarrow E[X|\mathcal g]\ in \ \mathcal L^1$$
What I have tried:
Use Scheffe lemma…
Focus
- 1,204
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2 answers
Expected Dice Rolling (EDITED)
Q- What is the expected no of rolls of a Dice to get a 6 CONDITIONED that all previous rolls ( if any) were even numbers ?
How I attempted this question - We would have a series of 2,4 which would terminate to 6. Sample space - (2,4,4,6) ,(6),…
Valay Shah
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Difference between expectation conditionally on a sigma-algebra and conditionally on the Borel sigma-algebra
I have no idea how to solve the following problem:
Consider the probability space $([0,1], \mathcal B([0,1]), \lambda),$ where $\lambda$ is the Lebesgue measure and $\mathcal B([0,1])$ stands for the Borel sets of $[0,1].$ Let $X(\omega) = \omega$…
Bling-Bling
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Step in proof $E_\theta T^*=E_\theta T$ of Rao-Blackwell
Say we have $T$ an estimator for $g(\theta)$, and $T^*=T^*(V)$ an estimator that only depends on the sufficient statistic $V$. My book claims the following:
$$
E_\theta TT^*=\sum_{v}E(TT^*\mid V=v)P_\theta(V=v)=\sum_vT^*(v)E(T\mid…
Sha Vuklia
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How to calculate conditional expectation $E[X|X \geq 0]$?
I only find some materials relating to conditional expectation like $E[X|Y=y]$.
How to calculate conditional expectation $E[X|X \geq 0]$?
user462102
- 23
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Conditional expectation of coin flipping
A fair coin is flipped successively until head appears for the second time. What is the expected number of flips necessary?
I'm not sure if the heads appear in a row or non-consecutively? And how do I approach the problem in the latter case?
Thanks.
L.mak
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Is $E[Y_t | \mathcal{F_s}] = E[Y_t | Y_s]$?
Learning abstract conditional expectations has me a bit confused. If we take a process $Y$, let $\mathcal{F}$ equal its internal filtration, then why is $E[Y_t | \mathcal{F_s}] = E[Y_t | Y_s]$?
The first is the expectation of $Y_t$ given ALL the…
ImeanH
- 86
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Conditional expectation wrt random variable
I really cannot figure out what is wrong with the last line....
There seem to be three definitions at least for conditional expectation with respect to a random variable. I would like to know if they are equivalent in all or in whichever contexts.…
James Well
- 1,209
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Question on the norm of the conditional expectation operator
I'm reading this paper that's talking about the norm of the conditional expectation operator.
He starts by defining $\mathbb{E}[\ \dot \ |\mathcal{F'}]: \ L^2(X,\mathcal{F}) \mapsto L^2(X,\mathcal{F'})$ where $\mathcal{F'}$ is a sub-sigma algebra of…
user202542
- 851
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Conditional expectation $E[X^2|X>1]$
Given that $X$ is a exponential random variable. I want to calculate $E[X^2|X>1]$. I think it would be $E[(X+1)^2]$, but do not have any convincing explanation.
Sanwar
- 360
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Conditional Expectation of a random variable given sigma algebra is the same random variable
We define the conditional expectation of a random variable $X$ on a given probability space $(\Omega,\mathscr F, P) $ w.r.t a sub $\sigma$-algebra $\mathscr G$ is a random variable denoted by $E[X|\mathscr G]$ defined as random variable that…
Uday Kumar
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