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].
109,331 questions
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Encoding prefixes of infinite sequences.
We consider infinite binary sequences $x \in[0,1]$ via their binary expansion.
$O: \{0,1\}^* \rightarrow \{0,1\}^*$ maps finite binary strings to finite binary strings.
for a string $m$ we define:
$$
...
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Recurrence in an infinite maze
It's well-known that a random walk in two dimensions almost always returns to the starting point; equivalently it almost always visits every two-dim location. And in three dimensions, this is not ...
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Probability that 5 shots are fired in the same region and different region. [closed]
Five shots are fired randomly within a circle of radius R. The circle contains an inscribed square, which divides the circle into five distinct regions: the square itself (R1) and and four identical ...
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Expectation solution to 'potion chance' mechanic.
This is a question that came up to me about the game Slay the Spire's 'potion chance' mechanic. It also applies to various other similar mechanics in other games (perhaps with different exact numbers)....
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Which is the formula for calculating the entropy of a binomial lattice model?
Which is the formula for calculating the entropy of a binomial lattice model?
Intro
I am trying to understand the properties of a Binomial Lattice Model (BLM) defined as follows: for a probability $0\...
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Why does infinite time not guarantee reaching state $K$ in a biased random walk?
I am trying to wrap my head around a 1D random walk problem.
The Problem:
A monkey is sitting on the origin ($0$) of an integral number line. At every period $t > 0$, it moves $1$ step to the right ...
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Convolution of weighted dependent random variables
Edited to provide more specifics:
Let two continuous random variables, $X$ and $Y$, follow a joint probability distribution defined by $C(F_X(x), F_Y(y))$ where $F_X(x)$ and $F_Y(y)$ are the ...
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Change of variable formula for conditional expectations [closed]
Let $(\Omega,\mathcal A,P)$ be a probability space, and let $T:(\Omega,\mathcal A)\to (\Omega',\mathcal A')$ be measurable. Also, let $X,Y$ be real random variables on $(\Omega',\mathcal A')$, with $X$...
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Is this induction proof really accomplishing anything?
I am reading "Combining counterfactual outcomes and ARIMA models for policy evaluation". The paper uses ARIMA models to estimate causal effects of interventions in time series. My question ...
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Probability of a given number within range $[0, 1]$ to be rational [closed]
I don't really think it is possible to evaluate this, but I tried to, and my rough estimate was that the probability should be $<0.5$ as there are relatively more irrationals than rationals, but I ...
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How to visualize video-game “true hit” system probabilities?
Background
Video games often incorporate randomness through events that have specific probabilities of occurring. For example, an attack can have a 90% chance of landing.
Apparently, players’ ...
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Does a conditional contraction inequality imply an almost sure upper bound? [closed]
I am trying to prove a result and was able to reduce it to the following question. I am not sure whether the statement is true, and I would be grateful for either a proof or a counterexample.
Suppose ...
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Relationships among single-crossing, a uniform preservation property, and second-order stochastic dominance?
Let $F$ and $G$ be cumulative distribution functions on $\mathbb{R}$, and let $X \sim F$, $Y \sim G$.
Consider the following three properties:
Single-crossing from below: \
There exists $\bar{v} \in \...
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Probability Of Two Beads Being The Same Color [closed]
There are 9 beads in a bag, 3 are blue, 2 are red, and 4 are black. A bead is picked at random and replaced. A bead is again picked at random. Find the probability that both beads will be the same ...
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Bayes' Theorem and Mutual Exclusion
Imagine a city with two fueling sites: $S_1$ and $S_2$. The volume of fuel sold at the first site is $v_1$ and at the second site is $v_2$. It is known that to buy fuel one has to necessarily buy it ...
