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Questions tagged [binomial]

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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9 views

asymptotic distributon, posterior mean

Suppose $X \sim Bin(n, \theta)$, $\theta \in [0,1]$. Considering a prior distribution for $\theta$ from $Beta(a,b)$, we get a posterior distribution $\theta|X \sim Beta(a+X, b+n-X)$ and so we get the ...
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Binomial Distribution: From binary (0/1) to uniform [0,1] by change of N? [on hold]

I was just reading about the central limit-theorem and how the binomial distribution approaches the normal distribution with increasing N. Now I wonder if the step-size between [0,1] has a similar ...
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UMVUE for Binomial Parameter [on hold]

Given T=∑Xi has Binomial distribution with paramters n and p, how do I calculate the UMVUE for p^3? I looked into (UMVUE for Bernoulli). But could not understand what the UMVUE is.
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Using count (instead of proportion) data with cbind() in R… in both dependent and independent variables?

In a study I hypothetically conducted, I have the number of times individuals pressed an "A" button and the number of times they pressed a "B" button. I also recorded the numbers of times they made ...
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1answer
27 views

Interval width for truncated confidence intervals

I'm conducting a simulation study to compare different methods of constructing CIs for a single proportion. The traditional (Wald/Asymptotic) CI can estimate the upper and lower bounds above 1 and ...
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Using Binomial Distribution to Determine Overbooking

Given the situation below, what is largest number of reservations the spa should accept to ensure that the probability of having sufficient capacity (i.e. the number of customers who show up is higher ...
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1answer
24 views

How to test whether two binomially distributed variables come from the same distribution?

I have data where I have a set of pairs of integer, each binomially distributed, and I want to be able to test whether the observations came from different distributions, though I don't care what ...
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2answers
57 views

Finding the maximum and minimum variance of the sum of two Bernoulli events?

You are guessing the contents of two envelopes. Let $U_i$ be the event that you guess correctly. Your probability of guessing correctly for each envelope is $P(U_1) = P(U_2) = 3/4$. $U_1$ and $U_2$ ...
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Zelen's Play the Winner Rule Randomization Scheme [migrated]

Does anybody know how to implement this algorithm in R? I have a total of 100 patients that I need to randomize and I want to know what is the chance of a greater than 55%-45% split (i.e. 45 or fewer ...
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1answer
34 views

Why cannot the model $\frac {y_{i,j }} {N_{i,j } } = \beta_0 + \beta_1 X_i + e_{i,j }, \ y_{i,j}\sim B(N_{i,j},\pi_i)$ have constant variance?

The following example is taken from a book by Walter Stroup on Generalized linear mixed models, and are supposed to show some limitations on trying to write models in equation form. Let $y_{i,j } \...
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427 views

Why does the likelihood function of a binomial distribution not include the combinatorics term? [duplicate]

So the likelihood function for a binomial distribution is: Why is the likelihood function above not multiplied by a combinatorics term: n! / (x! * (n - x)!) If the likelihood function is ...
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1answer
37 views

Clinical trials simple randomization scheme simulation [closed]

I'm trying to do 1000 simulations for how to randomize 100 patients to two treatment groups (A and B) using simple randomization scheme (with probability 0.5) and figure out what is the chance of a ...
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How do I choose between binomial and Bernoulli family using brms in R

My research question is: is the rate of forgetting (slope) influenced by the degree of encoding? So I have three encoding degrees and three time intervals in which I test people using different items. ...
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18 views

expectation of binomial distribution problem [closed]

There are 100 sites arrange in a line. There are two strategies: Each site can have a 0.05 probability to be occupied. Each 25 sites must have one occupied. Here is the question: what is the ...
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1answer
43 views

How can I tell whether this is a negative binomial distribution or binomial distribution?

A scientist inoculates several mice, one at a time, with a disease until he finds 3 that have contracted the disease. If the probability of contracting the disease is 1/6, what is the probability that ...
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Derivation of variance of Odds Ratio in a 2x2 table

Assuming that the elements of a 2x2 table (a,b,c,d) are binomial in distribution with a being $Bin(n_1,p_1)$ and c being $Bin(n_2,p_2)$. How can we show that $\hat {var(logOR)} = \frac 1 a + \frac 1 b ...
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Simulating a 2x2 contingency table (cohort study)

I want to simulate a 2x2 contingency table with fixed row totals. I know that the distribution would be binomial but I can't seem to do it in a matter than constraints the randomly generated elements ...
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3answers
47 views

Bayes: How many heads given n flips?

I’m trying to wrap my head around a rather simple coin flip experiment. Say I have studied a coin and obtained a posterior for the probability of getting a head when flipping it. How do I then use ...
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How to use Binomial Distribution in clinical trials

I would like to ask your opinion about the use of a simple likelihood binomial estimation in a medical paper. DATA: Let assume to have 150 patients, each patient has been treated, thus we get an ...
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Why rare events carry much information? [duplicate]

Consider a non-symmetric coin experiment where $p$ is the probability to get heads. I flip the coin $n$ times and try to estimate the value of $p$. The amount of heads has the binomial distribution so ...
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1answer
43 views

Binomial Probability Distribution

I figured out a and b and just need help with question c, does my process below seem right? I am not sure if that is how the probability is determined p(x)= (n/x)p^x(1-p)^n-x (30/15)(0.5)^15(0.5)^15=...
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1answer
49 views

Generating Failure Times

I have 1800 units and I know the probability of failing for each unit every week for 2000 weeks. I would like to obtain some failure times for each unit. One way to do this could be to use a ...
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How to use MLE to infer N in binomial distribution? [duplicate]

I am learning how to use MLE methods to infer population parameters, and specifically need to infer N in the binomial distribution. From my understanding of MLE, the first step is to take the ...
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1answer
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Inquiry: Obtaining equivalent results between binom.test() in R and Proc Freq?

Problem I am reading the Wikipedia article on the binomial test and I have been unable to duplicate the purported R and SAS code showing they are equivalent. The p-value I get for R code is ...
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why can two random variables be added only when they have the same domain?

I am watching lecture 7 in harvard stats 110 and the professor is teaching distribution of addition of two random variables and in a breadth says that random variables can be added only if their ...
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178 views

Wikipedia's text about the Clopper-Pearson interval for binomial proportions

I'm trying to understand the following text currently (i.e., 2019-09-25) in Wikipedia about the Clopper-Pearson interval: The Clopper–Pearson interval is an early and very common method for ...
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1answer
25 views

Logistic regression with binomial independent variable

I have a table of observations, with three columns --- (a) class labels (can be 0 or 1), (b) counts of successes (out of a certain number of Bernoulli trials) and, (c) numbers of Bernoulli trials. I ...
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23 views

Interaction in a Binomial how interpret

So, my doubt is simple, I ran this model: glm(formula = pregnancy ~ Bull*SEMEN, family = binomial(), data = dt) Just 2 bulls (a and b) and 2 semen (s and c) ...
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27 views

Possible imbalance in binomial GLMM - weighting?

I'm attemtping to fit a binomial glmm to my data. I've been using lme4 and I'm somewhat confused about interpretting the results. I think you'll be able to answer my question pretty quickly, so ...
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1answer
56 views

Probability mass function of product of two binomial variables

I have two i.i.d. binomial variables $X$ and $Y$ with given $n$ and $p.$ What is probability mass function of $Z = X \times Y$? I need pmf as function $f(Z, n, p).$
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Issue with proof in Statistical Theory related to Beta and Binomial distributions [duplicate]

Assume $X_n$ is distributed $\text{Beta}(1/n, 1/n)$ and $X$ is distributed as $\text{Binom}(1,1/2)$. Show that $X_n$ converges to $X$ in distribution. I'm having some issue with this question. I ...
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1answer
30 views

X given Y is a normal random variable with mean Y and var 4. Y~Binomial(10, 0.6). Find E(X) and Var(X)

Is this a joint probability distribution? Can I assume X and Y are independent and that E(XY)=Y? I am stuck at this question.
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Whats the Probability of pulling 5 aces in 10 pulls with replacement

This is not homework. I am just going through the Bayesian Statistics the Fun Way book ( https://nostarch.com/learnbayes ) and I can't figure out how they come up with inputs for Chapter 4 question ...
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1answer
58 views

Normal V Binomial Distribution (Elementary Question)

CONTEXT: First year university statistics course exam question Suppose couples decide to have children until they either have a child of each sex, or they have three children. Assume that births are ...
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Binomial distribution for two groups if success rate is not given

Two groups of twelve statisticians are taught two different methods of Statistics. (Assume that a statistician in group one is matched in terms of their Statistics ability with a statistician in group ...
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1answer
21 views

Can I get a p-value testing statistical significance between two coin flipping rounds?

i'm a graduate student (biology program) with minimal experience with statistics. I have two questions relating to my project that i'd love help with! The first question is how I can take a single ...
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1answer
139 views

Discrepancies with Actual vs Expected Probabilities for Distribution?

I am attempting to estimate consecutive days worth of sales of specific items in each store: For most stores, the probability (n=1 k=1, n=2 k=2, etc…) that an item will continue to sell over a period ...
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2answers
109 views

How many trials are needed to get a statistically important proportion of 0.003 for a binomial variable?

I want to do an experiment and try to get an initial proportion (e.g., successful rate). The experiment will generate one of two results (either success or failure). I would like to know how many ...
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Confidence interval for population proportion estimate with replacement and known total population

So, I have an experiment that is equivalent to having a bag with $N$ balls of various colors in it, then drawing a ball, marking down its color and returning it to the bag. Repeat this process until I ...
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1answer
35 views

Determining the significance of rare events

We have been having a discussion about the significance of 2 accidents. If I have 2 groups: Group 1 is a baseline where an accident has occurred 70 times in 3,500,000 and Group 2 where an accident ...
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Approximation for the sampling error of the number of positive cases in a Bernoulli trial

Reading the book "Energy for Future Presidents" I found a way of approximating the binomial proportion sampling error which I never saw before, and I would like to know if my derivation is correct. ...
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Determining the sampling size ensure defect rate of less than X parts per million at a confidence interval

For quality sampling, I need to ensure a defect rate of less than 5000 parts per million, which is 1/200, at a specific confidence level. The goal is to have the smallest sample number for the ...
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1answer
26 views

Do I add both the new variable and the original variable to my log binomial model?

I'm calculating interaction indices for some variables in my model. I have an interaction between two variables (age (continuous) and hypertension (binary)), and I read in a similar publication that ...
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1answer
39 views

How do I interpret this interaction between a continuous variable and a binary variable from a log binomial model?

I'm new to modelling and not sure how to interpret this interaction for a results section. The model output tells me that the interaction between cancer (binary) and age (continuous - one year ...
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2answers
51 views

Binomial proportion confidence interval when rigid bounds on population proportion (0.5 < p < 1)

A standard problem is estimation of confidence intervals for a population proportion given that one has observed f successes out of n independent trials. There is a reasonable discussion of this ...
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23 views

How do I determine goodness of fit for a test of n binary decisions?

Let's say I have $n$ pairs of items. For each pair I select one item over another due to some perceived trait. This could be anything, for example, identifying which image is brighter than the other ...
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1answer
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What is the probabilty that X > 2 conditioning on Y = 2? (Homework)

another homework question here. Let 𝑌 be a binomial random variable with 10 number of trials and 0.2 probability of success. Let X be a uniformly distributed random variable over the interval [0, 3]. ...
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25 views

Are the beta distribution and binomial distribution related? [closed]

I've seen questions like this and this, but it hasn't quite answered my question. How intertwined are the Beta and Binomial distributions? A quick sidenote: the Poisson distribution and the ...
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1answer
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(Binomal Distribution) With n = 20, p = 0.2, calculate the probability that 2X >4 (Homework) [duplicate]

This is a homework question. The scenario is as follows: A dishwasher can accommodate 20 plates in one loading. With every loading, there is a 20% chance that 1 plate will not be cleaned properly. ...
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1answer
46 views

How to find P(2X>4)?

This is a Binomial question. I am required to find P(2X>4), and given that X~B(10,0.2), how do I convert it to 2X~B(n,p)? Have tried converting from P(2X>4) to P(X>2), but understand that it doesn't ...