Tagged Questions

The binomial distribution gives the frequencies of "successes" in a fixed number of independent "trials". Use this tag for questions about data that might be binomially distributed or for questions about the theory of this distribution.

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37 views

How to get a posterior distribution from Gamma and Binomial distributions [on hold]

I am investigating the time on book (t) before write off.The sample data consists of times taken until write off, however these times have been calculated from accounts that have been written off ...
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0answers
11 views

75% success, ranges for given sample sizes with 95% confidence

A given task has a 75% chance of success. With 90% confidence, what would be expected ranges of success for - 10 attempts - 50 attempts - 100 attempts - 1,000 attempts - 10,000 attempts very many ...
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1answer
16 views

Confidence Interval for the average of a set of proportions

If I have a dataset of 500+ observations (people in this case) that has the % of allotted dollars that were spent for each person (so, I have each persons allotted dollars and their dollars spent), ...
2
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0answers
33 views

Sum of Bernoulli random variables

I need some help with a homework assignment. The question I'm given is: "Suppose that $X_1, X_2,..., X_n, W$ are independent random variables such that $X_i\sim Bin(1,0.4)$ and $P(W=i)=1/n$ for $i=1, ...
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1answer
38 views

Power analyses of 5 populations of infection data (binomial data) [duplicate]

I am PhD Biologist. I have 5 populations of infected moth larvae (3 inbred, and 2 outbred). The infection in this case is spread vertically (from mother or father to offspring). Normally the virus is ...
1
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1answer
38 views

Statistical measure of international diversity

I've got a large collection of geotagged tweets, each linking to an article from a given author. For each author, I'd like to derive a number that describes how diverse is their list of tweeting ...
4
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1answer
27 views

Distribution of random sample of confidence intervals containing the true mean

Given 50 random samples, each of size 25, from a normal distribution with mean 20 and standard deviation 5. From each of the 50 samples, you can find a 90% confidence interval for the mean. Let Y be a ...
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0answers
16 views

The Binomial Distribution

I am trying to understand why when asked for the probability at least 1 success does it take the form 1-P(X=0) or 1-BINOM.DIST(0,1,.18,1). I am trying to understand this logic. Can you explain in such ...
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1answer
29 views

Questions about non-standard test statistic for difference of two population proportions

Background I'm considering the number of observed 'successes' $x_1$ and $x_2$ from $n_1$ and $n_2$ independent trials respectively. These counts can be considered realisations of random variables ...
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1answer
62 views

Bootstrapping probability of success: what is wrong with my method?

I have a dataset where each row represents the outcome of individual bets placed by a population of players; each row has two fields: a player identifier and the outcome of the bet (1 if the player ...
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3answers
55 views

For Y~B(11, 0.3) what is P(|Y-5| >= 3)?

I feel this is a simple problem, yet I cannot seem to solve it. Any help is greatly appreciated.
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6 views

Scaling Specificity to larger data set

Suppose I have the following 2x2 table ...
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0answers
32 views

Binomial Probability (Dice)

The throwing of a one or two is called a success. The six dice are thrown together 64 times and the frequencies of the throws with 0, 1, 2,..., 6 successes are summed over all six pairs are as ...
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1answer
11 views

Combining two estimates of p in a binomial estimation

I have an estimation problem for a binomial data. I got a sample and from that I can get an estimation. But I also have a kind of prior information about the p. But mind it, this prior is just a ...
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0answers
15 views

Binomial distribution - one-tailed

I am still struggling with a few questions regarding binomial distribution. Any help or ideas on how to solve them, would be very much appreciated!! Regards Ida N = 20. Determine the critical number ...
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1answer
26 views

Binomial distribution - coin toss

I would be really happy, if someone would explain how I solve this; Let p denote the probability for “head” in a coin toss, p = 0.5. The coin is thrown N times. What is the probability of the ...
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1answer
33 views

Evaluating a binomial (success vs. failure) glm

I'm familiar with (some) approaches to evaluating the fit (or accuracy) of a binary (logistic) model (e.g. AUC). Are there methods/approaches that are particularly well-suited for a binomial (success ...
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0answers
37 views

How to Calculate in Binomial Probability Distribution

I'm new to the Binomial Probability Distribution. I do not know how to calculate based on this formula below. Can you show me HOW to do it? ...
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0answers
12 views

cross-validate hierarchical model for binomial data that is often sparse

I have binomial data (e.g, 130 successes in 4000 trials). In many, if not most, cells of interest, there were few trials and thereby few successes (e.g., 0 successes in 35 trials, 1 successes in 18 ...
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1answer
24 views

The probability of a student getting a given question correct and the associated uncertainty (Item response theory)

I'm doing some statistics on multiple choice test scores (with item response theory, (http://en.wikipedia.org/wiki/Item_response_theory). I want to know the probability that a student with a certain ...
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0answers
16 views

Standard error of the mean for binomial dist [duplicate]

I know what intuitively what's going on but... We know that in general the standard error of the mean is $$ \sigma_\bar{X}^2 = \sigma_X^2/n $$ Right? But when I apply this to the binomial ...
2
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0answers
45 views

Fitting a logistic curve to cumulative data using glm()

I'm trying to fit a logistic curve to cumulative data, derived from satellite imagery. Previously, I have point observation data which were either 0s or 1s. Os being 'forest' and 1s being ...
3
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2answers
195 views

What are the advantages of a simulation over an exact binomial calculation?

Let's say that I want to calculate the probability of achieving more than 8 heads in 10 coin tosses. The easiest and most accurate way will be to simply use the binomial distribution and sum the ...
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1answer
49 views

Help for Binomial Distribution question

I am having issues with understanding a question on an assignment: A test for the presence of a certain disease has probability 0.05 of giving a false-positive reading and probability 0.04 of ...
2
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1answer
38 views

Upper bound for asymmetry using skewness

Can the following quantity be upper bounded by the (standardized third moment) Skewness of $X$ ($\mu_3/\sigma^3$)? $$\left|\mathbb{P}(X \geq \mathbb{E}X) - \mathbb{P}(X \leq \mathbb{E}X)\right|$$ I ...
2
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3answers
76 views

Counterexample against binomial assumptions

The question is from a Master-level Probability Course. It is well known that the underlying assumption for the binomial distribution is that there are n independent Bernoulli trials. More ...
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0answers
14 views

Dealing with an uncertain number of trials

I've got a binomial distribution where I'm trying to figure out the probability of success (specifically, the odds of a certain event in a video game). This would be simple enough, except that I ...
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1answer
52 views

Probability of a sum of values from a number of dice rolls

4 six-sided dice are rolled independently. Compute the normal approximation with continuity correction for the probability of rolling a total of at most 6. I have arrived at a point where I got that ...
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1answer
29 views

Find MLE by combining two different experiments

I am trying to solve the following problem on an assignment. Anna has two dice. Die $F$ is fair: it rolls $1,2,3,4,5$ or $6$ with equal probability $\frac{1}{6}$. Die $D$ is dodgy: Anna suspects ...
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0answers
34 views

Hypothesis testing with multiple variables

I'm trying to understand the process behind testing both A/B site changes for statistically significant increases in conversion rate, and also how then to expand this to testing multiple variables. ...
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0answers
25 views

binomial test for over-represented kmers in biological sequences - what is the right test?

Imagine you have a long string, like a genome, and you split it up into every overlapping word of size n. This is called a kmer. ...
2
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1answer
23 views

Estimation probability in related binomial distribution

I have two binomial experiments with an unknown probability - But i do know that the ratio between the probability in the first experiment and the probability in the second experiment - For example I ...
2
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1answer
65 views

Standard error of proportions, with weighting

I have a set of experiments $i=1\dots k$ each of which performs $n_i$ binomial experiments, recording a fraction $p_i$ successes. Clearly if I trust all of the experiments equally, my estimated ...
1
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1answer
46 views

Using the binomial distribution to identify chance-level responses

I have a subject who was giving 2-alternative forced choice responses for a task consisting of 80 trials. For each trial, there was a 50% chance for each of the two options to be correct. This means ...
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0answers
75 views

Problem solving a simple probability exercise

I'm currently studying a Statistics course and I'm trying to solve a simple probability exercise: A production facility employs: 20 workers on the day shift 15 workers on the swing shift 10 workers ...
6
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2answers
228 views

Why does SAS PROC GLIMMIX give me VERY different random slopes than glmer (lme4) for a binomial glmm

I am a user more familiar with R, and have been trying to estimate random slopes (selection coefficients) for about 35 individuals over 5 years for four habitat variables. The response variable is ...
1
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1answer
38 views

How to sample from “biased” binomial distribution (ideally in python/numpy)

I need to sample a variable from a distribution that's like a binomial distribution except with a "bias", I'm not sure what it may be called: $p(X=k)$ is proportional to $k.B(n,p)(k)$ where $B(n,p)$ ...
1
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1answer
68 views

How to model a count dependent variable with upper limitation

I have a dependent variable, which have 0, 1, 2, or 3 for its value. I asked participants to choose three items and coded 1 if it is in a certain category and 0 otherwise. I add the three binary ...
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2answers
231 views

Bayesian estimation of $N$ of a binomial distribution

This question is a technical follow-up of this question. I have trouble understanding and replicating the model presented in Raftery (1988): Inference for the binomial $N$ parameter: a hierarchical ...
5
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1answer
103 views

Estimating $n$ and $p$ for Binomial distribution, repeated counting of partly hidden population

A brief motivation: $n$ critters live in an aquarium, where sadly they often hide in, under or behind things. When the aquarium is observed, each critter is only seen with probability $p$ ...
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2answers
139 views

Test if two binomial distributions are statistically different from each other

I have three groups of data, each with a binomial distribution (i.e. each group has elements that are either success or failure). I do not have a predicted probability of success, but instead can ...
5
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0answers
55 views

Identifiability in generalized linear random effect model?

Suppose I observe binary $Y_{ij}$ for $i = 1, ..., N$ and $j = 1, ..., J$ and I want to model $$\Pr(Y_{ij} = 1 \mid \lambda_{i}) = \Phi(\lambda_{ij}), \qquad [Y_{ij} \perp Y_{ij'} \mid \lambda_i]$$ ...
3
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2answers
71 views

Posterior distribution of proportional difference of two binomial variables

Can somebody point me in the right direction for a treatment of the following problem? I imagine this should be a fairly common problem in medical statistics... Given two binomial random variables ...
2
votes
1answer
96 views

Formula for calculating sample size for hypergeometric distribution

Suppose you have an urn with "N" marbles. All marbles are either black or white. You take a sample of size "n" without replacing them to the urn. With this one sample you would like to be able to ...
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1answer
36 views

Binomial data and PCA and cluster analysis

I have obtained responses on around 48 items measuring employer attractiveness. The goal of my analysis is to cluster respondents according to these employer attractiveness dimensions. I plan to ...
4
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3answers
72 views

Analytic or sample standard deviation with binomial data

I've been looking for recommendations on whether it's better to use the sample standard deviation (SD) for a binomial distribution or use the analytic SD (or variance). It's for experiments with ...
0
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0answers
38 views

Correcting for multiple testing on non-independent sliding windows

Question Values taken from adjecent windows in a sliding windows are corrolated. If I calculate a p-value from each window, how can I correct for the fact I have tested many windows, given that the ...
1
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1answer
24 views

Comparing polynomials

I've got a bunch of data on pop singers' performance on the Hot 100 charts over time, and I'm trying to compare the early part of different artists' careers. For example, I might look compare Miley ...
3
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3answers
86 views

Binomial random variable conditional on another one

On the Wikipedia page for the Binomial distribution, the following property is mentioned (under the related distribution section): (paraphrased) If $X\sim \text{Bin}(n,p)$ and $Y|X \sim ...