Question

In which of the following should the random variable x not be modeled with a geometric distribution?

1) The number of trials until the first success in a sequence of independent Bernoulli trials
2) The number of failures before the first success in a sequence of independent Bernoulli trials
3) The number of successes until the first failure in a sequence of independent Bernoulli trials
4) The number of trials until the first failure in a sequence of independent Bernoulli trials

Answer 1

The number of successes until the first failure should not be modeled with a geometric distribution because this distribution characterizes the number of trials until the first success, which is not equivalent.

Step-by-step explanation:

The random variable x should not be modeled with a geometric distribution in situation 3) The number of successes until the first failure in a sequence of independent Bernoulli trials. The geometric distribution is characterized by having one or more Bernoulli trials with all failures except the last one, which is a success, meaning it models the number of trials until the first success, not until the first failure. Since the geometric distribution is defined as the number of trials until the first success (X~ G(p), where p is the probability of success), option 3 does not meet this requirement.