13.1.4. Cumulative Distribution Function (CDF)

Try these first

1. 1.

   What does the CDF represent?

   Hint

   Think about what kind of probability it describes.

2. 2.

   What is one property of a CDF?

   Hint

   Consider how the probability changes as the value increases.

3. 3.

   What is the cumulative distribution function?

   • A function for discrete variables
   • A function defining cumulative probabilities
   • A random variable

   Hint

   Recall what cumulative means.

4. 4.

   True or False: The CDF at positive infinity equals 1.

   • True
   • False

   Hint

   Think about certainty in probabilities.

5. 5.

   Given a continuous random variable with a PDF of f(x) = 2x for 0 ≤ x ≤ 1, determine the CDF and graph it.

   Hint

   Use the fundamental theorem of calculus for integration.

6. 6.

   Explain how CDFs can assist in decision-making within risk management frameworks.

   Hint

   Consider how probabilities directly inform decisions.