The bernoulli-distribution tag has no wiki summary.
2
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1answer
33 views
Detect bias in subset of Bernoulli processes
I'm looking for advice on the best method to use to answer this question.
General scenario:
We have multiple testing machines A,B,C,D etc. each tests a identical randomly selected part and provides ...
1
vote
1answer
44 views
Using continuity correction for normal approximation or not?
Below is a question on a recent actuarial exam, Exam 3L of the CAS. I didn't know whether or not to use the continuity correction when using the normal approximation to do hypothesis testing ...
0
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2answers
47 views
Find the expected value of $(\bar X_n-p)^3$
Let $X_1,X_2,\dots, X_n$ be a random sample from a Bernoulli distribution with parameter $p$. Let $\bar X_n$ be the sample average given by $\bar X_n=\frac{1}{n} (X_1+X_2+\dots+ X_n)$). Find the ...
2
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0answers
55 views
Why is it futile to use the deviance as a goodness-of-fit measure for Bernoulli data?
In Ordinal Data Modelling by Johson & Albert, page 102-103:
For Bernoulli observations [...] the asymptotic chi-squared
distribution of the deviance statistic may not pertain. Indeed, for
...
3
votes
3answers
133 views
The probability of getting one variation of consecutive outcomes in Bernoulli trials before another
Consider tossing a fair coin and writing down the outcomes in a sequence of symbols. "H" stands for head and "T" for tail. Let A , B and C be the words HTHH , HHTH and THHH respectively. What is ...
1
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0answers
9 views
Using known correlations to select a sample that maximizes model prediction
I want to model the outcome of a binary dependent variable D over a large universe [many records, 100s of variables].
Given a fixed sample size, I want to maximize the accuracy of the model over the ...
1
vote
1answer
85 views
exponential density & bernoulli distribution
I had asked a question on Maximum Likelihood earlier. Now I have two questions that are related to this question which had:
Let $x$ have an exponential density $p(x|\theta) = \theta e^{-\theta x} ...
7
votes
1answer
351 views
Empirical distribution alternative
BOUNTY:
The full bounty will be awarded to someone who provides a reference to any published paper which uses or mentions the estimator $\tilde{F}$ below.
Motivation:
This section is probably not ...
3
votes
2answers
119 views
How does the confidence interval for the parameter p of a bernoulli trial vary with the value of p itself?
This is a very basic question (I'm currently studying undergrad level statistics), but I was hoping for some clarification regarding an assertion I read in a newspaper article earlier today. The ...
3
votes
2answers
94 views
Flipping random coins from a bag - equivalent to a single coin?
My first and I think naive question here.
I am trying to model a certain business, and the simplest model I am willing to test is:
1. there is a bag of differently biased coins.
2. every step, a ...
0
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1answer
94 views
Compute a confidence interval for Bernoulli distribution
Given a Bernoulli distribution with a success probability of p = 0.02. Let's say we have N=3000 samples. How can I compute a confidence intervals for the expected number of successes (e.g., with 5% ...
3
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2answers
138 views
Dependent Bernoulli trials
The probability of a sequence of n independent Bernoulli trials can be easily expressed as
$$p(x_1,...,x_n|p_1,...,p_n)=\prod_{i=1}^np_i^{x_i}(1-p_i)^{1-x_i}$$
but what if the trials are not ...
0
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0answers
56 views
What do I need to know about Bernoulli distributions to build a Naive Bayesian classifier?
I'm building a naive bayesian classifier for a binary classification.
Right now I have an estimator for Bernoulli distributions, and real distributions (using a kernel mixture distribution).
I can ...
0
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0answers
90 views
Wilson's confidence interval for standard deviation?
I have a a set of films, and for each films, a set of reviews - varying between 1 review and several hundred reviews for each film. Each review has a star rating from 1 to 5.
I am using Wilson's ...
4
votes
1answer
162 views
How to show operations on two random variables (each Bernoulli) are dependent but not correlated?
I was looking at the following question from "One Thousand Exercises in Probability" by Grimmett, page 25, question 16 (not homework just self-study):
Let $X$ and $Y$ be independent Bernoulli ...
1
vote
1answer
121 views
Testing median, and distribution of Binomial
Given the median is $m>0$
We have $n$ random variables: $Y_1,Y_2,..,Y_n$
If we observe a value above $m$ then $Y_i=1$ if we observe a value below $m$ then $Y_i=0$
The probability of getting an ...
15
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3answers
289 views
K successes in Bernouli trials, or George Lucas movie experiment
I'm reading "The Drunkard's Walk" now and cannot understand one story from it.
Here it goes:
Imagine that George Lucas makes a new Star Wars film and in one test market decides to perform a crazy ...
1
vote
1answer
156 views
Calculating standard error for a Normal population
I'm a programmer, with a decent but not-expert knowledge of stats, and I'm working through these instructions for how to create funnel plots.
I understand from a previous question that the standard ...
1
vote
2answers
696 views
Expectation of a product of multiple random (Bernoulli) variables
I'm doing a research and using random variables to model a random process. I'm defining a Bernoulli random variable as a product of several other Bernoulli variables (three or more). So, I have the ...
1
vote
1answer
106 views
Basic information or texts required about modelling k bernoulli trials
I have been presented with a dataset comprised of individuals and the number of teeth they have had extracted. The maximum is 32, and almost half of the data are zeros. I have been asked to suggest an ...
-1
votes
1answer
101 views
A function of Bernoulli variables?
Let $X_1,X_2,...,X_n$ be a fixed number of Bernoulli random variables. My problem is to find a distribution for $Y$ such that for some function $f$, we have $Y=f(X_1,X_2,...,X_n)$. There are two ...
3
votes
1answer
96 views
Why is the expected value of the number of trials before the first success larger than the number of trials with a 50% probability of success?
For a Bernoulli distribution with parameter p, the number of trials with a 50% probability of at least one success is about (1/p) * ln(2). But the expected value of the corresponding geometric ...
-2
votes
1answer
104 views
Expected value of this Jackpot game [closed]
If there exists a fair National Lottery, that someone bets £1, Jackpot increases by £1, and there is p chance that he wins a Jackpot. If a Jackpot is won, it is reset to 0. repeats.
We can easily ...
2
votes
1answer
88 views
What is distribution of lengths of gaps between occurrences of ones in Bernoulli process?
Which distribution fits the following data? Data are generated by the process:
$X_t, \, t=1,2,3,\ldots,n$ is equal 1 with probability $p$ and 0 with probability $(1-p)$ for each $t$.
What is the ...
