12.10. Important Points to Remember

Try these first

1. 1.

   Define a discrete random variable and provide one example.

   Hint

   Think of outcomes that can be counted, not measured.

2. 2.

   What is a valid PMF?

   Hint

   Recall the three conditions we discussed in class.

3. 3.

   What does PMF stand for?

   • Probability Mean Function
   • Probability Mass Function
   • Partial Mass Function

   Hint

   Remember it focuses on discrete outcomes.

4. 4.

   True or False: The sum of the probabilities in a valid PMF is 0.

   • True
   • False

   Hint

   Consider the definition of a valid PMF and its requirements.

5. 5.

   You have a PMF where the probabilities are P(0) = 0.4, P(1) = x, and P(2) = 0.3. Determine x, ensuring the PMF is valid.

   Hint

   Think about the condition that they must sum to 1.

6. 6.

   Consider a discrete random variable X with outcomes from a set {1, 2, 3}. If P(X=1) = 0.2, P(X=2) = 0.5, what is P(X=3) needed for normalization?

   Hint

   Remember normalization requires the total probability to be 1.