Suppose we are counting successes in a Poisson process where we expect 12 successes per hour. What is the variance in the number of successes during a 25 minute period?

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**Question:**

Suppose we are counting successes in a Poisson process where we expect 12 successes per hour. What is the variance in the number of successes during a 25 minute period?

**Options:**

- 3
- 5
- 6
- 25

**Explanation:**

In a Poisson process, the variance is equal to the mean. To find the mean for a 25-minute period, we convert 25 minutes to hours: 

25 minutes = 25/60 hours ≈ 0.4167 hours.

The expected number of successes in 0.4167 hours is:

Mean = 12 successes/hour * 0.4167 hours ≈ 5.

Therefore, the variance is also 5. 

The correct answer is 5.
Transcribed Image Text:**Question:** Suppose we are counting successes in a Poisson process where we expect 12 successes per hour. What is the variance in the number of successes during a 25 minute period? **Options:** - 3 - 5 - 6 - 25 **Explanation:** In a Poisson process, the variance is equal to the mean. To find the mean for a 25-minute period, we convert 25 minutes to hours: 25 minutes = 25/60 hours ≈ 0.4167 hours. The expected number of successes in 0.4167 hours is: Mean = 12 successes/hour * 0.4167 hours ≈ 5. Therefore, the variance is also 5. The correct answer is 5.
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