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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Finding n and c in single sampling plan

I am learning a quality control course and in Single sampling scheme for attribute type inspection I don't understand the method used for calculating the values of $n$ and $c$. The method is as ...
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3answers
167 views

Logistic Regression - Error Term and its Distribution

On whether an error term exists in logistic regression (and its assumed distribution), I have read in various places that: no error term exists the error term has a binomial distribution (in ...
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0answers
17 views

What method to use in this cancer problem?

I am confused on what to do with this problem: "Suppose we identify fifty 50-to 54-year old women who have both a mother and sister with a history of breast cancer. Five of these women themselves ...
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0answers
14 views

Comparing the difference in proportions for 3 different groups

I conducted an experiment and just need some general guidance on where to go from here. I know I have to do some kind of binomial test on my data. Suppose I have the following data: ...
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1answer
45 views

Exact two sample proportions binomial test in R (and some strange p-values)

I am trying to solve the following question: Player A won 17 out of 25 games while player B won 8 out of 20 - is there a significant difference between both ratios? The thing to do in R that ...
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1answer
19 views

Computing mixture of Binomial distributions

I'm trying to model a simple Bayes net, with $n$ samples based on a (unobservable) Bernoulli parameter, representing a true state of the world. Let $T$ be a Bernoulli random variable, with ...
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109 views

Theoretical justification of choice for confidence interval exact method for the success probability parameter of negative binomial variable?

I have a computer experiment that runs the Bernoulli series with unknown probability $p$ of success. The experiment terminates when $m$ failures are observed. So, the unknown parameter $p$ has the ...
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1answer
157 views

Estimating parameters for a binomial

First of all I'd like to precise that I'm not an expert of the subject. Suppose to have two random variables $X$ and $Y$ that are binomial, respectively $X\sim B(n_1,p)$ and $Y\sim B(n_2,p),$ note ...
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1answer
77 views

Problem with urn

I'm reading Thinking fast and slow and there's this problem I cannot get a correct answer. Here it is: Half the marbles are red, half are white. Next imagine a very patient person (or a robot) ...
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1answer
64 views

How to compare the proportion female with the proportion male

I would like to know if it is correct to do the following statistical comparison: In a sample of $440$ patients, I have $241$ females ($54.8\%$) and $199$ males ($45.2\%$). Are these proportions ...
3
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1answer
63 views

Are these data underdispersed? If so, what mechanisms may explain this?

Say someone who is well practiced (appears to have reached a performance plateau) shoots 20 free throws on 15 different days and is successful the number of times shown in the upper histogram (...
2
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1answer
78 views

Can multinomial distribution be simulated by a sequence of binomial draws?

I wonder if single multinomial distribution (I will use the notation from JAGS/WinBUGS, but in fact, this is principial thing rather than of particular language) ...
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1answer
29 views

Testing for samples being drawn from identical Bernoulli r.v.'s

Suppose that I have a sequence of size $n$: $x_1,\ldots,x_n$, $x_i\in\{0,1\}$. My null hypothesis is that all $n$ members of the sequence are drawn independently from an identical Bernoulli ...
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1answer
45 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 ...
2
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1answer
18 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
38 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
47 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 ...
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1answer
40 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 ...
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1answer
32 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
18 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
34 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
66 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
62 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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7 views

Scaling Specificity to larger data set

Suppose I have the following 2x2 table ...
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1answer
46 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
13 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
16 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
34 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
41 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
15 views

Binomial Distribution's Syntax in R

About The Binomial Distribution and statistics R. dbinom(1:6, 7, 0.8) What is number 7? Is it population?
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0answers
15 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
26 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 ...
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0answers
57 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 ...
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2answers
205 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
53 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
39 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 ...
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3answers
83 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
57 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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35 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
26 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
74 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 ...
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1answer
49 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
87 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
280 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 ...
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1answer
49 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 $B(n,p)$ ...