# Tagged Questions

Questions relating to (pseudo)randomness, random oracles, and stochastic processes.

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### Probability of Finding Disconnected Patterns in Digit Positions of Random Integer Sequence

Let's say I have a random sequence of 9 digits. x x x x x x x x x What is the probability of finding '9' in the first position and '93' in the fourth and fifth ...
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### Empirical Process estimation using gaussian density and specific random generator

EDITED: To formulate into math framework: I have a sampling generator producing IID gaussian. To highlight the convergence in the distribution, I calculate the following error. Given a precision ...
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### The variance of a sum of random vectors

There are $n$ vectors each containing exactly $q$ random variables as elements. Each vector is denoted I$_k$. Each variable within the vector has its own (normal) probability distribution, and the ...
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### Expected number of weighings to get heaviest rock

You are given ten rocks and you would like to find the heaviest one. With each weighing you randomly select two of the rocks and determine which of the rocks is heavier. What is the expected number of ...
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### Generating random GPS probes

I'd like to generate a certain number of random GPS probes, with the following requirements: The coordinates (latitude and longitude) must be inside a circle with given center and radius. The ...
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### lim sup and lim infs of Brownian Motion: $B_t/\sqrt{t}$ as $t \to \infty$ or as $t \to 0$.

Below is my question. Q7.9 is what I'm stuck on. I've done Q7.8; I included it in the picture because I'll use it in Q7.9, and it gives a definition that I'll use. Update: This question is now solved,...
### What does it mean that a Monte Carlo (MC) algorithm is correct with probability at least $p$?
I was trying to understand the definition of what it meant to say that a Monte Carlo (MC) algorithm succeeds with probability at least $p$. Usually in probability I would have concluded that the ...