6.3 - Continuous Random Variables
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Practice Questions
Test your understanding with targeted questions
What is a continuous random variable?
💡 Hint: Think of examples like temperature or time.
Which function represents the probability of a continuous RV?
💡 Hint: Remember, it's a curve that describes probabilities.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What is the primary purpose of a probability density function?
💡 Hint: Think about what a PDF represents graphically.
The cumulative distribution function ranges from:
💡 Hint: Consider how probabilities are represented in total.
2 more questions available
Challenge Problems
Push your limits with advanced challenges
Given the PDF f(x) = 6x(1-x) for 0 ≤ x ≤ 1, calculate the expectation value E(X) and the variance Var(X).
💡 Hint: First find the integral for E(X), then use the result to find Var(X).
If a continuous random variable has a CDF F(x) = x^3 for 0 ≤ x ≤ 1, find the PDF and verify it integrates to 1.
💡 Hint: Differentiate the CDF to find the PDF, then integrate.
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