Respuesta :
Answer:
The probability mass function (pmf) of X is:
[tex]P(X=k)={{k+r-1}\choose k}\cdot (1-p)^{k}\cdot p^{r};\ k=1,2,3,...[/tex]
Step-by-step explanation:
The random variable X is said to be a Negative Binomial random variable.
The random variable X 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 X is:
[tex]P(X=k)={{k+r-1}\choose k}\cdot (1-p)^{k}\cdot p^{r};\ k=1,2,3,...[/tex]
Here,
k = number of successes
r = number of failures
p = probability of success
