8.2.2 - Continuous Random Variables
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Practice Questions
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Define CDF and how it is used for continuous random variables.
💡 Hint: Think of how you define probabilities.
What does it mean for a function to be non-decreasing?
💡 Hint: Consider how this looks on a graph.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What is the main purpose of a CDF?
💡 Hint: Think about what the CDF computes.
Is the CDF for continuous variables a jump function?
💡 Hint: Consider the properties of continuous functions.
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Challenge Problems
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Given a continuous random variable with the PDF defined as f(x) = 6x(1-x) for x in [0,1], derive the CDF F(x).
💡 Hint: Use integration by parts or the power rule.
Consider a random variable X with the CDF defined as F(x) = x^3 for x in [0,1]. What is its PDF?
💡 Hint: Recall the relationship between CDF and PDF.
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