For questions about the expectation of a random variable: computations, upper/lower bounds, etc.
Questions tagged [expectation]
3734 questions
2
votes
1 answer
Expectation; example of infinite sum?
My book gives the following definition for expectation:
If $X$ is a discrete random variable, the expectation of $X$ is
denoted by
$\mathbb{E}(X)$ and defined by $\mathbb{E}(X)=\sum_{x \in
> Imx}x\mathbb{P}(X=x)$
whenever this sum converges…
Sha Vuklia
- 3,960
- 4
- 19
- 37
2
votes
2 answers
Proof for Mean of Geometric Distribution
I am studying the proof for the mean of the Geometric Distribution
http://www.randomservices.org/random/bernoulli/Geometric.html
(The first arrow on Point No. 8 on the first page).
It seems to be an arithmetico-geometric series (which I was able to…
Starlight
- 1,680
2
votes
1 answer
How many pupils sees the wall?
In a school class there are 30 pupils with different height. They form a queue and let us say that a pupil in the queue sees the wall if there is no taller people in the front of him or her. Otherwise he or she sees the neck or back of an another…
selfstudying
- 23
2
votes
2 answers
Expected gems needed to level up
There is a game where you have an item and you can raise the level of the item from +0 to a higher value.
To do this you have to spend a Gem. First 6 upgrades are 100% successful. The 7th upgrade has a 50% chance of successfully raising the item 1…
1
vote
1 answer
law of iterated expectations with nested conditioning sets
What I'm given:
$\bf{g_i}=\bf{x_i}$$u_i$ where $\mathbf{x_i}$ is a k-dimensional vector
and
$E(u_i|\mathbf{g_{i-1},...,g_1})=0$
I want to show that $E(u_i|u_{i-1},...,u_1)=0$
My work so…
guest028
- 13
1
vote
2 answers
How to find expectation of geometric distribution?
On average 1 in 8 people in a particular community is left-handed and the rest are right-handed. A
sample of people is chosen at random, one by one, until a left-handed person is obtained. Find the
probability that the number of people in the sample…
Leon
- 33
1
vote
1 answer
Expectation of multiplication of dependent variables
Let $N(t)$ have Poisson distribution with parameter $\lambda t $ (meaning, expected value of $\lambda$ events per hour. What is the expectation of:
$N(6) \cdot N(10)$? (The expected value of the number of events in 6 hours multiplied by the number…
Shmoopy
- 325
1
vote
2 answers
Expectation question
Since $E(X-\mu)^2=Var(X)$, expanding both sides we get $E(X^2-2X\mu+\mu^2)=E(X^2)-[E(2X\mu)-E(\mu^2)]=E(X^2)-[E(X)]^2$.
How is $E(2X\mu)-E(\mu^2)=[E(X)]^2$? What is $E(\mu)$ and $E(\mu^2)$?
user373534
- 135
1
vote
1 answer
Expectation value of exponential of a function - first two moments of function known
I have a function $f(t)$ and know that $\langle f(t)\rangle=0$ and $\langle f(t)f(t')\rangle=C(t-t')$;
Now i want to calculate:
$$\left\langle\exp\left(\int\limits_{0}^t f(t') \, \mathrm{d}t'\right)\right\rangle$$
I tried to look at the sum…
Martin
- 191
1
vote
0 answers
solution by iterated expectation
Considering the problem
There were n couples attending a ceremony. Out of the 2n people,
exactly m of them ate pizza, chosen randomly over all subsets of 2n
people. Let X be the number of couples that didn’t eat pizza. Find an
explicit…
Sajad
- 23
1
vote
1 answer
Ten balls are put in 6 slots at random. Then what is the expected total number of balls in the two extreme slots
I am having the difficulty to predict the probability for this problem to find the total number of expectations.
Priyanka
- 437
1
vote
1 answer
There is a result that $E(X)$ exists iff $E(|X|)<\infty$
I have a question on an interesting property of $E(X)$
There is a result that $E(X)$ exists iff $E(|X|)<\infty$
The if part is true because, in that case we get a series which is absolutely convergent , so the original series must converge.
But what…
user321656
1
vote
0 answers
A Fair Dice is Rolled. Find the Expected Value of the Roll.
This method is used from the expectation of a discrete variable. Would this be right?
E(X) = (1 * 1/6) + (2 * 1/6) + (3 * 1/6) + (4 * 1/6) + (5 * 1/6) + (6 * 1/6)
E(X) = 1/6 (1+2+3+4+5+6)
E(X) = 21 / 6
E(X) = 7 / 2
dj5
- 29
1
vote
0 answers
Expectation value of empiric copula
I need the expected value of the empirical copula.
I have for a fix $\mathbf{u}=(u_1,\dots,u_d) \in [0,1]^d$
$\mathbb{E}[C^n(\mathbf{u})] = \frac{1}{n} \sum_{i=1}^n \mathbb{E}[\mathbf{1}(\tilde{U}_1^i \le u_1,\dots,\tilde{U}_d^i \le u_d)]…
Fluffy
- 11
1
vote
2 answers
Why are $E[X]_, \;E[Y]= 0$ if $X_,\; Y$ are measured from their means?
I was studying some examples of linear correlations where I got the reasoning:
Since $X_,\;Y$ are measured from their means, $$E[X]= 0=E[Y]$$ ....
Can anyone tell me why it is so?
user142971