# Questions tagged [probability]

For basic questions about probability and for questions about calculating a probability, expected value, variance, standard deviation, or similar quantity. For questions about the theoretical footing of probability (especially using [tag:measure theory]), ask under [tag:probability-theory] instead. For questions about specific probability distributions, use [tag:probability-distributions] instead.

68,544 questions
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### States of the world/Game theory and Beliefs

This post consists on 3 parts: the question itself, hint and a table. The question will make sense to you only after you have read the tables and the hint attached. The problem is about beliefs of a ...
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### probability of dependent events of box of balls

I have a box full of $N$ unique balls. The first time, I pick $k$ balls out of this box (I inspect them and put them back). On the second time, I also pick $k$ balls out of the same box (that has $N$ ...
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### Are there similar theorems to the Infinite Monkey Typewriter Theorem?

I was thinking about the Infinite Monkey Theorem and wondered if there’s any similar theorems but with a finite set? I know the infinite size is a critical assumption in the Monkey theorem, but are ...
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### Independence of Records of Permutation

For any permutation $\sigma = (\sigma_1,\dots,\sigma_n)$, call $\sigma_k$ a record if $\sigma_k>\sigma_i$ for $1\le i\le k-1$. Let $\alpha_k$ be the indicator for the event that $\sigma_k$ is a ...
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### In a sports competition, ten athletes of different nationalities challenge…

In a sports competition, ten athletes of different nationalities challenge each other in the javelin throwing. Let $X$ be the distance covered by the javelin of the Italian athlete and suppose it is a ...
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### “expectation of sum is sum of expectation”, is this claim true? if yes, how to justify this claim?

this post is saying linearity of expectation gives following equation $$\mathbb{E} [\sum_{j\neq i} Y_i Y_j] = \sum_{j\neq i} \mathbb{E} [Y_i Y_j]$$ per wiki, Linearity of Expected_value is ...
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### conditional probability about gambler winning x amount of coins

A gambler plays seven games one after the other and the chance to win each of them is $\frac{1}{3}$, independently of the others. For $k = 1, ..., 7$, if the gambler wins game number $k$, then the ...
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### Inverse transform sampling from Poisson to Exponential

I have a Poisson disributed r.v. $$X\sim Poiss(\lambda)$$ and want to transform it to an exponentially dist. r.v. $$Y\sim Exponential(\lambda),$$ by using the inverse transform sampling method. I ...
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### probability of drawing two card simultaneously

For e.g what is the probability that both card drawn from a deck of card will be king. Is drawing two card simultaneously and drawing one after the other(not replaced back), the same thing. Because ...
Here the context : I'm a bit confuse by the notation, since he defines $Y_t=Y_t^x$, and at the bottom, he says that $R^x$ is the probability that $Y_t$ start at $x$, and after he writes $$R^x(Y_{t_1}\... 2answers 1k views ### Sample Space & Combinations/Permutations This is the question: "List the sample space for three individuals chosen at random to vote either Democrat or Republican. List the distinct combinations and permutations." These are what I got for ... 0answers 19 views ### Probability of a name to be in the “Firstname Lastname” order I am trying to figure if a name is in the "Firstname Lastname" order, knowing the probability of each name to be either a firstname (class A) or a lastname (class B). In other words, given two ... 0answers 8 views ### probability limit of log chi sqaured I have the following: Prob\left(T \cdot ln(1+\chi_{1})>ln(T)\right) \rightarrow 0 where \chi is a chi-squared distribution with 1 degree of freedom and T is an arbitrary real number and the ... 1answer 19 views ### If \tau=\inf\{t>0\mid B_t\notin B(0,R)\} does |B_{\tau}|\leq R or |B_\tau|\leq R a.s.? Let (B_t) a Brownian motion starting at 0 and let B(0,R) the open ball of radius R. Let \tau=\inf\{t>0\mid B_t\notin B(0,R)\}. Does |B_\tau(\omega )|\leq R for all \omega  or we only ... 0answers 12 views ### Cindy spins this spinner 300 times. work out an estimate for the number of times that Cindy will get L? I spin a spinner 80 times. The table shows information about the results Outcome/Frequency J / 39 K / 25 L / 16 Cindy spins this spinner 300 times. ... 0answers 18 views ### Conditional summations in probability Consider the following problem, from Tijms's Understanding Probability: Nobel airlines has a direct flight from Amsterdam to Palermo. This particular flight uses an aircraft with N =150 seats. ... 1answer 23 views ### Generate various PDFs (probability theory, statistics) How can one most easily generate PDFs (probability density functions) with various shapes (say with 1,2,3,... etc. local maximums)? I mean... let's say I want to generate various continuous ... 0answers 38 views ### If S_n is Binomial (n,p) then \mathbb P(S_n=k)\approx \frac{(np)^k}{k!}e^{-np}. I was reading this post, and I have to admit that I was quite confused. The question was : If S_n is a Binomial r.v. with parameter (n,p) s.t. n large, p very small and np not to big (for ... 0answers 14 views ### Simplifying the summation of fractions of Gamma functions I am trying to simplify this summation, but I have no idea how. I have tried using the fact that$$\sum_{i = 1}^n \frac{\Gamma\left(a + i\right)}{\Gamma\left(i\right)} = \frac{n\Gamma\left(a + n + 1\...
I am aware that Boole's inequality can be proved by induction. How do we extend these results to an infinite set? (since induction cannot be applied in this case) P($\bigcup\limits_{i=1}^{\infty} A_i$...