negative binomial rv is the number of failures that occur before the rth success in a sequence of independent and identical success/failure trials. The probability mass function (pmf) of X is

The probability mass function (pmf) of X is:

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:

Here,

k = number of successes

r = number of failures

p = probability of success

80π/3 or about 83.775

step-by-step explanation:

since a cone is 1/3 of a cylinder, we need to find the base's area. since area = πr^2, we get 16π. then, multiplying this by 5, we get 80π. dividing by 3, since the cone's volume is 1/3 of that of a cylinder's, we get 80π/3.

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answer: 2x + 2 − 2 = 10 − 2; subtraction property of equality

step-by-step explanation: