Modern theory of probability is formulated on the footing of measure theory. Use this tag if your question is about this theoretical footing (for example probability spaces, random variables, law of large numbers, central limit theorems, and the like). Use (probability) for explicit computation of ...

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Doubt about Probability of arranging identical balls

There are four boxes and 12 balls. The boxes are numbered and hence distinguishable but the balls are identical. What is the probability that a random arrangement would result in 10 balls in box 1 2 ...
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Conditions on Poisson random variables to convergence in probability

Let $X_1,X_2,...$ denote iid random variables such that $X_j$ has a Poisson distribution with mean $\lambda t_j$ where $\lambda$ > 0 and $t_1, t_2,...$are known positive constants. a)Find conditions ...
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How to get closed form solutions to stopped martingale problems?

Way back when, I took a course in stochastic processes in college. I remember being frustrated by the plethora of abstract proofs without much in the way of how to use them to get actual results. It ...
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Dose “optional stopping theorem” imply “optional sampling theorem”?

Suppose $X$ is a martingale,$\tau$ and $\sigma$ are two stopping times which satisfy (a)$\sigma\le\tau$ and (b)the "optional stopping theorem" holds,that is to say: $$\mathbb E[X_\sigma]=\mathbb ...
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Probit regression model: Construction of weighted least squares algorithm

I'm posting a difficult general linear model question which I would like to solve. Question: Consider a probit regression model for $y \in ${$0,1$}:$E(y|x)=\Phi(x'b)$, where $\Phi$ is the standard ...