What happens to the Mean of a geometric distribution as the probability of…
2025
What happens to the Mean of a geometric distribution as the probability of success (p) increases ?
Answer: A. It decreases — Step-by-Step Solution To understand how the mean of a geometric distribution changes with the probability of success (p), we analyze its mathematical…
- A.
It decreases
- B.
It increases
- C.
It remains constant
- D.
It fluctuates
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Correct answer: A
Step-by-Step Solution
To understand how the mean of a geometric distribution changes with the probability of success (p), we analyze its mathematical definition.
Identify the Formula: The mean (expected value) of a geometric distribution, which models the number of trials until the first success, is defined as:
Mean = 1 / p
Analyze the Relationship: * The probability of success (p) is in the denominator.
As the value of p increases (meaning success becomes more likely), the denominator gets larger.
Dividing 1 by an increasingly larger number results in a smaller quotient.
Conclusion: Therefore, as p increases, the mean (the expected number of trials until the first success) must decrease.