8.3. Properties of the CDF

Try these first

1. 1.

   What does monotonicity of a CDF imply?

   Hint

   Think about how probabilities accumulate.

2. 2.

   What are the limits of the CDF at negative and positive infinity?

   Hint

   Consider the total probabilities.

3. 3.

   What does it mean for the CDF to be monotonic?

   • It only increases
   • It can decrease
   • It remains constant

   Hint

   Think about how probabilities add up.

4. 4.

   True or False: The CDF approaches 0 as x approaches positive infinity.

   • True
   • False

   Hint

   Consider the behavior of total probability.

5. 5.

   Given a randomized experiment where outcomes can be represented in a discrete CDF with jump discontinuities, describe how you would derive the PDF.

   Hint

   Focus on differentiating the jumps.

6. 6.

   In what scenarios would you expect a right-continuous CDF to be advantageous in modeling real-world scenarios?

   Hint

   Consider applications in stochastic processes.