8.1. What is a Cumulative Distribution Function (CDF)?

Try these first

1. 1.

   Define a Cumulative Distribution Function.

   Hint

   Think about what F(x) represents in terms of probability.

2. 2.

   What is the range of a CDF?

   Hint

   Consider the nature of probabilities.

3. 3.

   What does the CDF F(x) represent?

   • Probability that X > x
   • Probability that X = x
   • Probability that X ≤ x

   Hint

   Think of the role CDF plays in distribution.

4. 4.

   True or False: The CDF can take values outside the range of 0 to 1.

   • True
   • False

   Hint

   Reflect on the nature of probability.

5. 5.

   Consider a random variable X with the PDF f(x) = 3x² for 0 ≤ x ≤ 1. Find the CDF F(x) and evaluate F(0.5).

   Hint

   Remember to adjust the limits of integration properly.

6. 6.

   A six-sided die is rolled. Calculate the CDF for the random variable representing the number shown on the die.

   Hint

   Create segments in your computation for clarity.