12.3. Properties of PMF

Try these first

1. 1.

   What does the non-negativity property mean?

   Hint

   Think about if you can have a negative chance of an event happening.

2. 2.

   Why is normalization important in PMFs?

   Hint

   Recall PMF like a cup; it must be full!

3. 3.

   What is the property that ensures probabilities are not negative in a PMF?

   • Normalization
   • Non-Negativity
   • Discrete Domain

   Hint

   This property safeguards the logical foundation of probability.

4. 4.

   Is a PMF valid if the total probabilities sum to more than 1?

   • True
   • False

   Hint

   Revisit the 'full cup of probability' analogy.

5. 5.

   Consider a scenario where a random variable X represents the number of correct answers from a multiple-choice exam with 3 questions (each question has 4 choices). Construct a PMF for X.

   Hint

   Identify the variable outcomes and apply the binomial distribution.

6. 6.

   Why might we prefer using a PMF over a PDF when analyzing data involving customer choices (like size selections: small, medium, large)?

   Hint

   Think about the nature of customer choices and their specific outcomes.