Final answer:
The standard deviation of a negative binomial random variable with r successes and a success probability of p is calculated using the formula σ = √(rq/p²).
Step-by-step explanation:
The standard deviation of a negative binomial random variable represents the measure of dispersion or variability around its mean. For a negative binomial random variable, we can denote it as X~NB(r,p) where 'r' is the number of successes desired and 'p' is the probability of success on each trial. The standard deviation σ of such a variable can be calculated using the formula σ = √(rq/p²), where 'q' is the probability of failure (q=1-p). It's important to note that the negative binomial distribution is similar to, but distinct from the traditional binomial distribution X~B(n,p), which has a different calculation for standard deviation, specifically σ = √(npq).