12.6. Cumulative Distribution Function (CDF) vs PMF

Try these first

1. 1.

   What does PMF stand for?

   Hint

   Think about the type of probability it deals with.

2. 2.

   True or False: The CDF gives probabilities for discrete outcomes only.

   Hint

   Consider the definitions of PMF and CDF.

3. 3.

   What does the PMF provide?

   • Probability of specific values
   • Cumulative probabilities
   • Both

   Hint

   Remember the definition of PMF.

4. 4.

   Is the following statement True or False? The CDF is used to find the probability of discrete outcomes.

   • True
   • False

   Hint

   Think of what CDF does.

5. 5.

   Suppose a discrete random variable has a PMF given as P(X=1) = 0.1, P(X=2) = 0.2, P(X=3) = 0.4, and P(X=4) = 0.3. Construct the corresponding CDF and explain the interpretation.

   Hint

   Add the PMF probabilities cumulatively to form the CDF.

6. 6.

   Consider a scenario where the CDF of a random variable is defined piecewise. Describe how this affects the PMF.

   Hint

   Analyze the areas where the CDF changes values.