Answer:
The probability mass function (pmf) of X is:
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:
Here,
<em>k</em> = number of successes
<em>r</em> = number of failures
<em>p</em> = probability of success