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marta [7]
2 years ago
7

negative binomial rv is the number of failures that occur before the rth success in a sequence of independent and identical succ

ess/failure trials. The probability mass function (pmf) of X is
Mathematics
1 answer:
astra-53 [7]2 years ago
8 0

Answer:

The probability mass function (pmf) of X is:

P(X=k)={{k+r-1}\choose k}\cdot (1-p)^{k}\cdot p^{r};\ k=1,2,3,...

Step-by-step explanation:

The random variable <em>X</em> is said to be a Negative Binomial random variable.

The random variable <em>X</em> is defined as the number of failures in a series independent and identical Bernoulli trials, before a specific number of success takes place.

For example, consider rolling a 5 on a six-sided die as the success and any other number as failure. Then the number of rolls before 5 occurs three times in a row can be defined as a negative binomial experiment.

The probability mass function of a negative binomial random variable <em>X</em> is:

P(X=k)={{k+r-1}\choose k}\cdot (1-p)^{k}\cdot p^{r};\ k=1,2,3,...

Here,

<em>k</em> = number of successes

<em>r</em> = number of failures

<em>p</em> = probability of success

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