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Questions tagged [negative-binomial]

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

262 questions
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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 distribution with the data?
Dara
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Joint Distribution, Geometric Distribution

Let X and Y be IID Geom(p) (independent and identically distributed geometric probability) and $N=X+Y$. Find the joint PMF (probability mass function) of $X,Y,N$. I know the solution to this but I could not come up with it myself, and even after…
Lillys
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Negative binomial distribution problem!

Every year for Halloween, it is estimated that $5$ out of every $8$ houses give away candy. (a) If we want to receive candy from $5$ different houses, what is the probability that we will need to visit at least $10$ of them? I tried using a negative…
Jose soriano
  • 55
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Is there a smart way to compute $\sum^{25}_{k=0}\binom {3000}{k} p^k (1-p)^{3000-k}$?

I am trying to compute probability, and I give a: $$\sum^{25}_{k=0}\binom {3000}{k} p^k (1-p)^{3000-k}$$ $$p=0,0001$$$ Is there a smart way to compute it? Another else, I am thinking about Poisson. What do you think?
user180834
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Negative Binomial Distribution questions

In 2016, Red Rose tea randomly began placing one of ten English porcelain miniature figurines in a l00 bag box of the tea, selecting from ten figurines in the American Heritage Series. (a) On the average, how many boxes of tea must be purchased by a…
Jemma
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CDF of a random variable with mulitple conditions

I am trying to solve a particular problem involving multiple conditions on a random variable. We have $X_1, X_2....$ such that $X|K = k_i$ is a negative binomial with number of success given by $max(k-k_i,0)$ with success probability q where k is…
Resting Platypus
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Negative binomial distribution - find the probability that 7 games will be played

Suppose that two teams are playing a series of games, each of which is independently won by team A with probability p and by team B with probability (1-p). The winner of the series is the first team to win i games. If i = 4, find the probability…
Daniel
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Problem with Negative Binomial Distribuition

Suppose two players A and B are trying to hit a basket of basketball. The probability that A hit at a given pitch is p, and he insists on the throws until he hits r times. The probability that B matches a given release is mp, where m is an integer…
Wecsley Prates
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Binomial theorem and series

I want to confirm some points about binomial series. The expression must be of the form$(1+x)^n$. $x<1$ The part where I am confused is that while finding derivatives through first principle , i've come through cases where binomial series is…
Diaga AoS
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Distribution of sum of correlated negative binomials

Is sum of two negative binomial variables also distributed as negative binomial if they are non-idependent and correlation is $ < 1$? Or not?
den2042
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Mass function; negative binomial distribution

I want to prove that the mass function of the negative binomial distribution satisfies that it adds up to $1\;\forall x\in\mathbb R$. My textbook starts as follows: $\displaystyle\sum_{k=n}^{\infty}\left(\begin{array}{l}k-1 \\ n-1\end{array}\right)…
Sha Vuklia
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