For questions about the expectation of a random variable: computations, upper/lower bounds, etc.

# Questions tagged [expectation]

3755 questions

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### Combinatorial reasoning in an expected value problem

I saw this problem:
There is an urn with $a$ red and $a$ blue balls. We are drawing from it without replacement until we have drawn all the blue balls (we know there are $a$ of them). What is the expected value of the number of balls remaining in…

Nesa

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### Can one tell based on the moments of the random variable if it is continuos or not

Suppose we are given moments of a random variable $X$.
Can we determine based on this if the random variable is continuous or not?
We also assume that the moments of $X$ completely determine the distribution of $X$.
In other words, do moments of…

Boby

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### Expectation of Last Remaining Container

You decide to play a holiday drinking game. You start with 100 containers of eggnog in a row. The 1st container contains 1 liter of eggnog, the 2nd contains 2 liters, all the way until the 100th, which contains 100 liters. You select a container…

Erik Godard

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### Expected Value of Square Root of Poisson Random Variable

Find the expected value of $\sqrt{K}$ where $K$ is a random variable according to Poisson distribution with parameter $\lambda$.
I don't know how to calculate the following sum:
$E[\sqrt{K}]= e^{-\lambda} \sum_{k=0}^{\infty} \sqrt{k}…

Susan_Math123

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### The Price is Right optimal play

The following situation happened on the Price is Right and I was curious about the optimal response.
The rules are:
A contestant rolls a wheel with 5 cent increments from 5 - 100 (20 numbers total). A contestant can choose to spin the wheel once and…

mathewbruens

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### Why are stochastic processes with decreasing expected value called supermartingales?

I am curious to know why a process which has decreasing expected value is called a supermartingale.
From a beginners perspective it would seem reasonable to have the following picture:
________ (increasing) above ==> super
…

user13247

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### linearity of expectation in case of dependent events

I could understand the linearity of expectation in case of independent events, but why does it work in case of dependent events too. It seems counter - intuitive. In case of dependent events, each outcome influences subsequent outcomes, hence they…

Shivmitra Mishra

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### Probability: Escaping Prisoner Question

Question: A prisoner in a dark dungeon discovers three tunnels leading from his cell. Unbeknownst to him, the first tunnel reaches a dead end after 50 feet and the second tunnel reaches a dead end after 20 feet, but the third tunnel leads to freedom…

AZ0987

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### Expected value of size of subset

Given a set $S$ such that $|S|=n$,
A random item is chosen randomly from $S$, and being appended to a new set $T$.
This process is being repeated $n$ times (with repetition), what is the expected value of $|T|$ ?

Uri Goren

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### The Expectation of a function of independent random variables

Assume we have for some index $i>n$ ($n \in \mathbb{N} $) the following ${\it Independent \ Random \ Variables}$ $$h_i \sim \text {i.i.d }\ \ \mathcal{CN}(0,1) \ \ \text{ Complex Gaussian}$$ $$\Omega_i \sim \text {i.i.d with pdf }\ \…

Henry

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### Expected number of cycles in permutation

Consider a random permutation of $1,2,\ldots,n$. What is the expected number of cycles in it? I thought about using linearity of expectation, but here it's not clear how we can break down the main random variable into different ones.

boaten

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### Does taking expected value of two sides of inequality maintain the inequality?

As some operations are not necessarily valid for maintaining an inequality (such as raising both sides of $-2 < 2$ to an even power), I wondered if taking the expected value of both sides is actually fine.
So, let's say $X$ is a random variable and…

Friedman

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### Example of a general random variable with finite mean but infinite variance

Given a probability triple $(\Omega, \mathcal{F}, \mu)$ of Lebesgue measure $[0,1]$, find a random variable $X : \Omega \to \mathbb{R}$ such that the expected value $E(X)$ converges to a finite, positive value, but $E(X^2)$ diverges.

Matt

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### Probability of number of people who know a rumor

Suppose that among a group of $n$ people, some unknown number of people $K$ know a rumor. If someone knows the rumor, there is a probability $p$ that they will tell it to us if we ask. If they don't know the rumor they will always say they don't…

Max

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### Random solving of a Rubik cube .

After playing a little with a Rubik cube I thought of the following problem :
Suppose we start with a solved Rubik cube (a general one , with $n^3$ cubes) . Then we choose one of the moves , each having a probability of $\frac{1}{6n}$ of being…

user252450