What is the primary difference between the geometric and binomial distributions?

• Binomial distribution is used for the first success.

• Binomial distribution is used for continuous data.

• Geometric distribution is used for multiple successes.

• Geometric distribution is used for the first success.

How is the mean or expected value of a geometric distribution calculated?

• 1 divided by the probability of success

• Probability of failure divided by success

• 1 divided by the probability of failure

• Probability of success divided by 1

What does the standard deviation formula for the geometric distribution involve?

• Square root of p divided by q

• Square root of q divided by p

• Square root of p times q

• Square root of q times p

In the geometric distribution, what does the probability formula q^(x-1) * p represent?

• Probability of success on every trial

• Probability of the first success on the x-th trial

• Probability of failure on the x-th trial

• Probability of multiple successes in x trials

Why are trials considered independent in the geometric distribution?

• Because the outcome of one trial does not affect another

• Because all trials have the same outcome

• Because each trial affects the next

• Because trials are dependent on previous results

In the traffic light example, what is the expected number of red lights before a green one?

• 7 lights

• 5 lights

• 3 lights

• 10 lights

What is the standard deviation of the number of lights before hitting a green one in the example?

• 4.47 lights

• 2.5 lights

• 5.5 lights

• 3.5 lights

What is the probability of the third light being the first green one in the example?

• 0.128

• 0.256

• 0.512

• 0.640

What is the probability of failure in the traffic light example?

• 1.0

• 0.2

• 0.5

• 0.8

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