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.

69,126 questions
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New Two Children problem

The well known "Two Children problem" is answered in " In a family with two children, what are the chances, if one of the children is a girl, that both children are girls?" What about this variant: ...
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Two weighted coins, determining which has a higher probability of landing heads

A friend of mine asked me the following question, and I am not sure how to solve it: You are given two weighted coins, $C_1$ and $C_2$. Coin $C_1$ has probability $p_1$ of landing heads and $C_2$ ...
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Coin Betting Expectation

Suppose I have a biased coin with probability of heads p, and tails q=(1-p). It is then used in a game which lasts at most N tosses, and start with a stake of £1. Each time the coin is tails my money ...
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Discovering properties of a graph by means of random walk

Suppose I have a regular, undirected, non-bipartite, finite, connected graph on $N$ vertices. Some fraction $\frac{c}{N}$ of the vertices are coloured gold, the rest are coloured black. If I let you ...
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Do the moments characterize a distribution with compact support?

Given a random variable $X=(X_1,...,X_p)$ with $P(X \in M) = 1$ for compact $M$, do the values of $E[X_1]$, $E[X_2], ..., E[X_1^2], E[X_1 X_2],..., E[X_1^3],...,E[X_1 X_2 X_3]...$ determine the ...
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3 other extensions of the Secretary Problem

In the classical secretary problem (also known as Marriage, Sultan's Dowry, Gogol problems), 1) There are $n$ candidates ordered from the best to the worst (no ties). We know $n$. 2) The candidates ...
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Matching Hats AND Coats Problem

Suppose $N$ men throw their hats in a room AND their coats in an other room. Each man then randomly picks a hat and a coat. What is the probability that: None of the men select his own hat and his ...
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Probability of having at least 'k' marbles specific to each of 'm' bags filled by sampling with replacement

I'm going to rewrite my original question to make it a bit clearer: Assume I have some set $P$ with $||P|| = N$ unique elements. I also have $S$ multisets, $(m_1, ..., m_S)$, of cardinality $L$, ...
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Prove that P(A|B,C)=P(A|C,B) after applying the Bayesian updating process

Prove that P(A|B,C)=P(A|C,B) after applying the Bayesian updating process. That is, prove that the order in which the information is presented does not matter.
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How do you compute the steady state probabilities of a continuous time markov chain?

Given a markov model with transition rate matrix $Q$, where the probability of each state at time $t$ is given by $P(t) = P(0)e^{Qt}$, where e is the matrix exponential, the steady state probabilities ...
Yesterday I asked you whether there's a situation where $E[X]$, $E[Y]$ defined, but $E[X\cdot Y]$ ($E[Z]$) is $\infty$ or even Diverging? You claimed that the answer is NO and it is not ...