# Questions tagged [bernoulli-process]

The tag has no usage guidance.

46 questions
Filter by
Sorted by
Tagged with
1 vote
48 views

### 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 ...
19 views

### Converting likelihood ratios hypothesis test from equality to inequality

I have the following LR test for proportions (to anyone familiar to applied statistics in finance, this is known as the Christoffersen's unconditional coverage test). We would like to know if $\pi$ is ...
• 53
15 views

### For n Bernoulli trials whose outcomes are 1 or -1, what is the PMF of the sum of n trails being r

Let $x_1, x_2, ...$ be iid with probability $p$ of being 1 and $1-p$ of being -1. Let $S(n) = \sum_{i=1}^n x_i$ and $S(0)=0$ Find $P(S(n)=r)$. My attempt: At first this looks like a normal Bernoulli ...
• 101
58 views

### 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 $k$ ...
• 527
83 views

### 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: ...
• 121
12 views

### 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 ...
11 views

### 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 ...
• 1
1 vote
40 views

### 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: $$P(A<B) \ge 95\%$$
• 1,048
18 views

### 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 ...
1 vote
54 views

### 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?
• 11
792 views

### 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 ...
• 280
145 views

### 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%...
• 151
209 views

### 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 ...
• 556
1 vote
80 views

### 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 ...
• 135
1 vote
50 views

### 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, ...
• 1,078
1 vote
80 views

• 339
821 views

### 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 ...
91 views

### 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 ...
• 835
153 views

1 vote
132 views

### 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 ...
2k views

### 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 ...
140 views

### 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 ...
• 155
189 views

We repeatedly make an experiment where we count the number $n$ of Bernoulli trials of known probability $p$, until some number of successes $s$ is reached. I'm willing to restrict to $p<0.01$ and $... • 189 60 votes 13 answers 50k views ### Does 10 heads in a row increase the chance of the next toss being a tail? I assume the following is true: assuming a fair coin, getting 10 heads in a row whilst tossing a coin does not increase the chance of the next coin toss being a tail, no matter what amount of ... • 601 2 votes 1 answer 395 views ### Bit Error Rate - Multiple Bernoulli trials with different probabilities If you transmit a sequence of bits over some line, errors may creep in. For instance, if the Bit Error Rate of this line is 1%, on average, every 1 out of 100 bits will flip to the opposite value. ... • 504 1 vote 0 answers 27 views ### Bounds on binary event estimation [duplicate] I would like to paint an objective picture of some binary outcome. Now I have data like this: 1085x yes, 1704x no. The percentage of the positive outcome is 40.72%, but I want to give an estimation ... • 458 2 votes 1 answer 1k views ### Sum of Beta-Bernoulli variables Assume you have$x_i \sim \operatorname{Bernoulli}(p_i)$with$p_i \sim \operatorname{Beta}(\alpha,\beta)$. I am exploring$Z=X_1+ \dots +X_n$According to this page, it is$Z \sim \operatorname{...
• 1,297
I am stuck with a very simple question, but I don't really understand sampling, so please help me. Assume that I perform Bernoulli sampling with parameter $q$ on data D, and obtain sample S1. Then on ...