8.2.1. Discrete Random Variables

Try these first

1. 1.

   What does the CDF measure?

   Hint

   Think about what CDF stands for.

2. 2.

   If a die is rolled, what is the PMF for each number from 1 to 6?

   Hint

   Since it's a fair die.

3. 3.

   What is the main purpose of the CDF?

   • To find the average value
   • To measure cumulative probabilities
   • To determine variance

   Hint

   Think about how it accumulates values.

4. 4.

   True or False: The CDF can sometimes decrease.

   • True
   • False

   Hint

   Consider the property of accumulation.

5. 5.

   Suppose we have a biased die with the following PMF: {1: 0.1, 2: 0.2, 3: 0.4, 4: 0.1, 5: 0.1, 6: 0.1}. Calculate F(4). What does this tell you about the probabilities related to outcomes less than or equal to 4?

   Hint

   Sum the probabilities for outcomes 1 through 4.

6. 6.

   In an engineering application, a component’s life expectancy follows the PMF {<1 year: 0.15, 1-2 years: 0.25, 2-3 years: 0.4, >3 years: 0.2}. Determine the CDF at the end of 2 years and discuss its significance.

   Hint

   Consider all probabilities up to the 2 years range.