A binomial random variable is defined to be the number of units sampled until x successes is
observed.

Name: A binomial random variable is defined to be the number of units sampled until x successes is observed.
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A binomial random variable is defined as the number of successes in a fixed number of trials, not until a certain number of successes is observed. The description given matches a negative binomial distribution, not a binomial distribution.

A Binomial Random Variable Is Defined to Be the Number