12.7. Applications of PMF in Engineering

Try these first

1. 1.

   Define the Probability Mass Function (PMF).

   Hint

   Think about how PMF relates to the probabilities of outcomes.

2. 2.

   What types of variables does PMF apply to?

   Hint

   Remember what 'discrete' means in the context of random variables.

3. 3.

   What does PMF represent?

   • Probability of an event occurring
   • Probability of a discrete random variable equaling a value
   • Mean value of a distribution

   Hint

   Recall how PMF quantifies specific outcomes.

4. 4.

   True or False: PMF can be used for continuous random variables.

   • True
   • False

   Hint

   Think about the definition of PMF.

5. 5.

   A digital communication system experiences a 5% packet loss during transmission. If 100 packets are sent, calculate the expected number of packets successfully received and use PMF to describe the distribution.

   Hint

   Think about calculating expectations from probability distributions.

6. 6.

   Consider a reliability system that predicts vehicle failures. If the system states that there is a 20% chance that a vehicle will fail in the first year and a 10% probability of a second-year failure, how would you use PMF to express these probabilities for future planning?

   Hint

   Focus on how to express discrete probabilities as a function of time.