8.2.1 - Discrete Random Variables
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Practice Questions
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What does the CDF measure?
💡 Hint: Think about what CDF stands for.
If a die is rolled, what is the PMF for each number from 1 to 6?
💡 Hint: Since it's a fair die.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What is the main purpose of the CDF?
💡 Hint: Think about how it accumulates values.
True or False: The CDF can sometimes decrease.
💡 Hint: Consider the property of accumulation.
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Challenge Problems
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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.
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.
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