6.4 - Examples and Applications
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Practice Questions
Test your understanding with targeted questions
What value can a discrete random variable take?
💡 Hint: Think of counting outcomes.
What is the expected value of rolling a fair six-sided die?
💡 Hint: Add up all possible outcomes and divide by total outcomes.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What is the PMF for a discrete random variable?
💡 Hint: Think about how probabilities are distributed for outcomes.
TRUE or FALSE: Continuous random variables can take any value within an interval.
💡 Hint: Refer to the nature of continuous data.
1 more question available
Challenge Problems
Push your limits with advanced challenges
A factory produces light bulbs with a defect rate of 10%. Define a discrete random variable X representing the number of defective bulbs in a sample of 10. Calculate its expected value and variance.
💡 Hint: Use the binomial distribution.
A random variable X has a PDF defined as f(x) = 3x² for 0 ≤ x ≤ 1. Find the expectation and variance of X.
💡 Hint: Remember to compute both E(X) and E[X²] for variance!
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