# Questions tagged [negative-binomial]

Questions about the negative binomial distribution, a discrete probability distribution.

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### Tim plans to attempt exam until pass. Chance of passing each time is $20\%$. Find probability that he needs to attempt atleast $2$ & atmost $5$ times

Question : Tim is in no hurry to graduate. He intends to write his last exam until he passes it, but he is too lazy to study. He estimates that the chance of passing the exam each time is $20\%$. ...
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### Why does negative binomial not apply [closed]

so there this question that A telephone saleswoman arranges a sequence of interviews of potential customers in order to sell them an insurance policy. She believes that her success rate in completing ...
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### Probability mass function of alternative Negative binomial distribution

I have a random variable $X$ defined by the sum of $k$ independent geometric distributions ($Y$) with parameter $p$, which makes it a negative binomial random variable $NB(k,p)$. The probability mass ...
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### How to test whether a negative binomial distribution fits my data using the (a, b, 0) methodology?

Question One thousand policies were sampled and the number of claims per policy were recorded in the table below: ...
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### Why does Negative binomial expansion have infinite terms

Why does negative binomial expansion have infinite number of terms and not equal to the example given below Why is $(x+a)^{-2}$ not equal to $\frac{1}{x^2 + a^2 + 2ax}$? ?
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### How to make negative binomial distribution model based on data?

I have a set of data that has actual frequency. I have difficulty to find the method of building the negative binomial distribution model. How to relate the parameters in negative binomial ...
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### Why use Negative Binomial distribution to model count data?

According to Wikipedia: https://en.wikipedia.org/wiki/Negative_binomial_distribution In probability theory and statistics, the negative binomial distribution is a discrete probability distribution ...
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### Expected value of a continous generalization of the negative binomial distribution

Let the random variable $X$ be the number of independent Bernoulli trials needed to reach $r$ failures when the probability of success is p. Then $X$ follows a negative binomial distribution \begin{...
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### Confusion about relationship between geometric and negative binomial RV's

(Geo for geometric random variable, NB for negative binomial) Let $X_1,\ldots,X_n\sim\text{Geo}(1/n)$ be i.i.d and let $X=\sum_{i=1}^nX_i$, I saw on wikipedia that $X\sim\text{NB}(n,1/n)$. However, ...
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### What Variance equation is this textbook using?

I'm doing a question on a Gamma/Poisson mix, which turns into a negative binomial. What I don't understand is the answer to the question - most of the answer makes sense to me (normal approximation ...
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### Binomial expansion of negative exponent in descending powers of x [closed]

Expand ${(1+x)}^{-2}$ in descending powers of x including the term ${x}^{-4}$
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### Question regarding Probability of Dice [closed]

A pair of dice is thrown 180 times in a row. Find the probability that the event is 25 or more times I should define random variable $X$ but is this binomial distribution or negative binomial ...
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### Confusion on how extended binomial theorem works

So I just finished learning the standard binomial theorem and I've just come across the extended (newtons binomial theorem). As expected I am completely baffled about how it works I do not understand ...
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### Negative binomial (and multinomial) extension to the minimum(failures,successes)

The negative binomial distribution defines the probability of N draws to obtain K successes. The negative multinomial gives the joint over k1...km given k0 successes. I need to find the PMF over n ...
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### Lower index of binomial coefficient becoming negative upon solving

The question While solving this question by using the property: r nCr = n n-1Cr-1 The value of lower index becomes negative which is invalid How do I proceed?
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### Marginal Dirichlet Negative Binomial Distribution and the Multinomial Inverse Polya Urn

I have the following 'URN-like' problem - assume an urn the contains balls with m different colors. As in the standard Polya scheme, every time a ball is sampled, it is returned the urn in addition ...
On this webpage, the expansion of the negative binomial series is given below. $$(x+a)^{-n} = \sum^\infty_{k=0} (-1)^k \begin{pmatrix}n + k - 1\\k\end{pmatrix} x^ka^{-n-k}$$ when $|x| < a$. My ...