# Questions tagged [bernoulli-process]

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### Use a sequence of bernouli trials to find the possibility of an event happening

I have the data below and We have a game, that has a prize jackpot. The jackpot prize starts at 1,000 credits and every round you play the jackpot increases, until someone wins the jackpot and it ...
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### Binomial Proportions when sampling without replacement not studied?

Question When doing surveys with a population, we obviously don't replace by design. Why is it then that the mathematics and statistics described in textbooks seems to be veering more on the side of ...
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I was studying some statistics in DataCamp and they assigned me this exercise that I can't solve. I tried speaking with people that know more statistics than me and we can't seem to agree in an answer....
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### Length of a bernoulli process to get a fixed amount of tails

I have the following Bernoulli process: Initial state: H = 0, T = 0 I launch a coin where probability of head is p. If I get head, then H = H + 1. If I get tails, then T = T + 1. I repeat the ...
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### Does the hypergeometric distribution follow a Bernoulli process?

There is a comment in an online resource that I need help understanding: In a Bernoulli process, given that there are M successes among N trials, the number X of successes among the first n trials ...
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### Bernoulli process and two exponentials

Suppose that a very long Bernoulli process gives a sequence with possible values: $A$ with probability $p$, and $B$ with probability $1-p$. The expected fraction of contiguous sequences of length $k$ ...
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### Rendering Bernoulli sampling by the binomial distribution

I want to characterize the simple algorithm for selecting, say, 20% of a discrete set when the total size of the set is not known: ...
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### How can I calculate the probability of K zero-crossings occurs in Bernoulli process at given length L?

In the Bernoulli process B[k] = 1(prob. p), -1(prob. (1-p)), the probability of B[n] !=B[n-1] will be (B[n] = 0 && B[n] = 1) + (B[n] = 1 && B[n-1] = 0) = 2p(1-p), so the probability ...
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### Number of Samples for Accurate Measure of Heavily Weighted Coin

I see articles on how to prove the "fairness" of a coin by flipping it N times. Using the estimator of true probability p=h/(h+t) along with a target max error and confidence interval, you ...
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### How many samples to state $P(A < B) \ge 95\%, A, B \sim \text{Bernoulli}$? [closed]

Suppose I have two series of samples: $$A \sim Be(p)$$ $$B \sim Be(q)$$ How may samples samples do I need to state that: $$P(A<B) \ge 95\%$$
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### PDF of estimated Bernoulli parameter

This is my first question on this part of the stack exchange, so please bear with me and correct me if I am missing something obvious. Statistics is not my main field of expertise. Background I wish ...
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### Standard Deviation of Bernoulli trials / Bernoulli process with different probabilities

If 20 independent Bernoulli trials are carried out each with a different probability of success and therefore failure, what is the standard deviation of the result? How is this calculated?
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### confidence intervals for the Poisson process ($\lambda$) sampled with uncertainty

Say, I have a Poisson process which was measured $N$ times, and each measurement produced $k_i$ value. Also, $k_i$ are events that I have to detect and my detection probability is $p$. In fact, I ...
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### Flat "geometric distribution" by varying the probability of the Bernoulli trail

In a simulation I am working on, each day (time step) there is a chance that a condition changes (at which point it is stuck in the changed condition). Setting this probability to a fixed value (say 5%...
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### How to calculate uncertainty of probability derived from random samples?

I'm running many simulations based on random samples, each of which produces a True or False result. The goal is to calculate the probability that the result will be True, which I can easily ...
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### Bernoulli Cusum Chart?

Can I use the R package named 'cusum' to make bernoulli cusum charts or should I use another package? I've been asked to explore using Bernoulli cusum chart for trending a parameter that's usually 0 ...
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### How can Bayes avoid Cromwell?

I'm studying widgets and their failures. Generally a widget will run for many years without trouble, but 1-2% of widgets will fail in a given year. I have a table which lists widget manufacturers (A, ...
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### How to determine minimum sample size for Bernoulli trials at a given confidence level?

I want to determine whether the true bounce rate of an email campaign (an email sent to many recipients) is <20%, at the 99% confidence level. I can send one "test batch" of randomly selected ...
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### Is average stopping time a continuous function of Bernoulli parameter?

Consider an infinite sequence $X = (X_i)_{i \in \mathbb N}$ of i.i.d. Bernoulli random variables with (unknown) parameter $p \in (0,1)$, and let $N$ be a stopping time on $X$. Is it always the case ...
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1 vote
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### How many Bernoulli trials to have N successes in series with restarts?

Bernoulli trials are sequences of 0 and 1. What is the average length, the number of trials, that you need to perform until you reach n ones in sequence? I tried to make it with a 2D recursion Here ...
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### What is the value of π in this experiment(Bernoulli)?

Experiment: You roll a fair 6-sided die 5 times. Define the random variable x = number of times you rolled an even number. The probability of exactly X successes in n trials for a Bernoulli process ...
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### Number of trials necessary to demonstrate Bernoulli process doesn't have mean p

I have a Bernoulli process that purportedly has mean $x$ but I hypothesize that the process actually has mean $q$. How many trials are necessary to demonstrate (to some confidence $p$) that the actual ...
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