For questions about the expectation of a random variable: computations, upper/lower bounds, etc.
Questions tagged [expectation]
3734 questions
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What's a real life example of a case in which the conditional expectation is not zero, but the non conditional expectation is zero?
If I had to give an example to my grandmother of such a case, what would be a good real life example for a case in which
$ E[u|x]\neq 0 \quad \text{and} \quad E[u]=0 ?$
Thanks!
Kiwile
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3 answers
Can we write $E[x_1x_2]^2$ in terms of $E[x^2_1]$ and $E[x^2_2]$?
when $x_1$ and $x_2$ are dependent, we know that $E[x_1x_2]^2 \neq E[x^2_1]E[x^2_2]$.
Is it possible to express $E[x_1x_2]^2$ in terms of $E[x^2_1]$ and $E[x^2_2]$?
I only know that $\quad var[x_i]=E[x^2_i]-E[x_i]^2$ and…
Lee
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the expectation notation
Hi I am going through some definition and proofs of Uniform integrability. I am just confused with these two notations: E(|$X_\alpha$|;|$X_\alpha$|>K) and E(|$X_\alpha$| $|$ |$X_\alpha$|>K); Are they equal? To my understanding, they seems both…
JINGYA HAN
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Expectation of picking a number from a uniform distribution
Ms. A selects a number X randomly from the uniform distribution on $[0, 1]$. Then Mr. B repeatedly, and independently, draws numbers $Y_1$,$Y_2$,.... from the uniform distribution on $[0,1]$ until he gets a number larger than $X/2$, then stops. The…
Meera Unni
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Explain the notation in the tower law
The tower law states:
$$\mathbb{E}(X)=\mathbb{E}[\mathbb{E}(X|Y)]$$
But, from my understanding, we have the following:
Suppose we let $Z:=X|Y$ and $a,b\in\mathbb{R}$. Then:
$\mathbb{E}(X)=a$ is the expectation of a random variable, so it is a…
YinWai Tse
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Expected Value of drawing 10 tickets
In a lottery, 10 tickets are drawn at random out of 50 tickets numbered from 1 to 50. What is the expected value of the sum of numbers on the drawn tickets?
My approach -
If after drawing a ticket, if it was replaced, then it can be easily solved.…
vishalgoel
- 127
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4 answers
It is the case that $E[\exp(X)] = \exp(E[X])$?
Is it the case that $E[\exp(X)] = \exp(E[X])$, where $X$ is a random variable?
I know this is too simple, but I must be googling the wrong things.
Ben S.
- 505
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1 answer
Finding 4th Moment of a Random Variable.
In an attempt to derive something, I have come to a point where I need to know what the following can be simplified to. It looks to me that I am looking for the 4th moment of ''y''. I am just not sure how to go about…
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Expected Value dice rolling
You roll a die until you get the number five. What is the expected value of the maximum roll you see(don't include 5, we only consider rolls upto and before the 5). I created a solution to this problem, although I am still confused because of the…
GTOgod
- 570
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1 answer
Check my solution for an Expected Value Lottery Problem
You have a lottery number with ten slots. On each slot is an equally probably number from 0 to 1. You are paid the maximum number of the ten slots. What is the expected payout of the lottery number.
My strategy was to use the integral definition for…
GTOgod
- 570
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1 answer
Expectation of exponential function
Let $X \sim \mathcal N(\mu, \sigma^2)$ which denotes some random costs. By making the investment $k > 0$ one can change costs to $Y(k) \sim \mathcal N(e^{-k}\mu,e^{-2k}\sigma^2)$ such that costs changes from $x$ to $y(k) + k$. I have from a paper…
clueless
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Expected length of unit segments
Suppose we draw $x, y, z$ from the uniform distribution on $(0, 5)$. How would we calculate the expected value of $|(x, x + 1) \cup (y, y + 1) \cup (z, z+1)|$?
user41281
- 554
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0 answers
Expectation of product of two Vasicek distributed variables
It's shown in a research paper that:
$$
E\left[ \Phi\left(\frac{\Phi^{-1}(PD)-\sqrt{\rho_{1}}Y}{\sqrt{1-\rho_1}}\right) \times \Phi\left(\frac{\Phi^{-1}(LGD)-\sqrt{\rho_{2}}Z}{\sqrt{1-\rho_2}}\right)\right]= \Phi_2\left( \Phi^{-1}(PD),…
bozhao
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1 answer
Expected Value of E(x) with two cdf's $F(x)\leq G(x)$
A random variable X is distributed in [0, 1].
Mr. Fox believes that
X follows a distribution with cumulative density function (cdf) $F : [0, 1]\rightarrow [0, 1]$ and Mr. Goat believes that X follows a
distribution with cdf $G : [0, 1]…
user405925
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Expected value of maximum of discrete and continuous random variable
Just looking for confirmation of what I believe to be true. Let $\tilde{x}\in\{x^L,x^H\}$ with $Pr(x^L)=p$ and $Pr(x^H)=1-p$. Also let $\tilde{y}$ be a continuous random variable with unspecified distribution function. Then, is the following…
John
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