What is the area under f(x) if the function is a continuous probability density function?Question 6Answera.1.0b.2.5c.1.5
Question
What is the area under f(x) if the function is a continuous probability density function?
Question 6
Answer
- a. 1.0
- b. 2.5
- c. 1.5
Solution
To determine the area under the curve of a continuous probability density function (PDF), we apply the core properties of probability distributions.
Step 1: Understand the Properties of a PDF
- A continuous probability density function must satisfy the property that the total area under the curve across its entire range is equal to 1. This is because the total probability must equal 1.
Step 2: Analyze Options
-
Given the options:
- a. 1.0
- b. 2.5
- c. 1.5
Among these, only option a (1.0) aligns with the fundamental definition of a probability density function.
Step 3: Conclusion
- Since the integral of the PDF over its entire range must equal 1, the area under the function f(x) is:
Final Answer
1.0 (Option a)
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