7.2.3. Cumulative Distribution Function (CDF)

Try these first

1. 1.

   Define the CDF in your own words.

   Hint

   Think about how probabilities accumulate.

2. 2.

   What is the relation between PDF and CDF?

   Hint

   Integration leads to cumulative values.

3. 3.

   What is the primary function of a CDF?

   • Describes likelihood at a point
   • Used for integration alone
   • Gives cumulative probability

   Hint

   Recall what cumulative means.

4. 4.

   True or False: As x approaches negative infinity, the CDF approaches 1.

   • True
   • False

   Hint

   Think about total probability discounting small values.

5. 5.

   Derive the CDF for a PDF given as f(x) = e^(-x) for x ≥ 0.

   Hint

   Set up the definite integral for the PDF.

6. 6.

   For a bimodal distribution with two peaks, how would you outline a method to derive its CDF?

   Hint

   Think about piecewise functions.