Questions tagged [probability]
For questions about probability. independence, total probability and conditional probability. For questions about the theoretical footing of probability use [tag:probability-theory]. For questions about specific probability distributions, use [tag:probability-distributions].
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Ants on a Stick Probability Question
One hundred ants are dropped on a
meter stick. Each ant is traveling either to the left or the right with constant
speed 1 meter per minute. When two
ants meet, they bounce off each other
and reverse ...
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Is the variance of the mean of a set of possibly dependent random variables less than the average of their respective variances?
Is the variance of the mean of a set of possibly dependent random variables less than or equal to the average of their respective variances?
Mathematically, given random variables $X_1, X_2, ..., X_n$ ...
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Mean of probability distribution
I have a probability distribution defined by the following density function:
$f(k,j,n,m)=\frac{(m n)! \mathcal{S}_k^{(j)}}{(m n)^k (m n-j)!}$ (With $\mathcal{S}_k^{(j)}$ being the Stirling number of ...
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The probability that no cup is upon a saucer of the same color
Six cups and saucers come in pairs: there are two cups and saucers that are red, white, and blue. If the cups are placed randomly onto the saucers (one each), find the probability that no cup is upon ...
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expected value of high-low guessing game
Assume a number between 1-100 (inclusive) is chosen randomly. You then attempt to guess the number. On each guess, if you didn't get the exact number, you're told whether the guess is higher or lower ...
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Understanding the proof of Th. 2.4, Probability in Banach spaces - Ledoux, Talagrand
I am reading the proof of Theorem 2.4 in the book "Probability in Banach spaces" by Ledoux and Talagrand. There's a lot of confusion so I really need help here.
And the proof is given below....
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Geometric distribution obtained from exponential distribution
I was trying to solve the following:
Let $\lambda>0$ and $X$ a random variable with $X \sim exp(\lambda)$. Show that $Y=[X]+1$ has geometric distribution of parameter $p=1-e^{-\lambda}$, where $[x]...
CommunityBot
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Taking Seats on a Plane
This is a neat little problem that I was discussing today with my lab group out at lunch. Not particularly difficult but interesting implications nonetheless
Imagine there are a 100 people in line to ...
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Probability of $Y+b > X$ for iid normal variables conditioned on a rare event
I am thinking of the (imprecise) claim that a small increase in the average ability in a population results in a large increase in the ability of the exceptionally able.
So I'm considering two ...
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An urn with 5 balls.
I am trying to fully understand the difference between two very similar problems. First I will state the problems. The first I will refer to as problem A and the second I will refer to as problem B.
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How can you visualize Independence with Venn Diagrams?
Imagine two events $A$ and $B$ that are not mutually exclusive, such that $P(A) = 0.3$ and $P(B)=0.4.$ Consider the Venn diagram of the two overlapping sets, and visualize moving them closer together ...
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Expected value of the gradient of logistic loss function to a normal distribution
Given a vector $\beta\in\mathbb{R}^d$, and a random vector $x\sim\mathbf{N}(0_d,I_{d\times d})$, that is $\{x_j\}_{j=1}^d$ are i.i.d generated from gaussian $\mathbf{N}(0,1)$, can we compute or ...
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Finding expectation of negative powers of the standard normal distribution
Problem
Suppose that $Z \sim \mathcal{N} (0, 1)$. Find $\mathbb{E}[Z^{-1}]$ and $\mathbb{E}[Z^{-\frac 1 3}]$ if they exist.
My working
Consider when $Z \geq 0$. Since $f_Z(z)$ is continuous at $0$ and ...
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General rule for finding out a probability distribution
I am trying to learn about how to find the probability distribution for functions of random variables in general.
Suppose we have a random variable $X$ with pdf $f_X$ and a random variable $Y$ with ...
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