9.2 - Summary
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Practice Questions
Test your understanding with targeted questions
What is the expectation of tossing a fair coin twice?
💡 Hint: Consider the probabilities of getting 0, 1, or 2 heads.
Calculate the expectation for a discrete random variable with values {1, 2, 3} and probabilities {0.2, 0.5, 0.3}.
💡 Hint: Use the formula E(X) = ∑x_i * p_i.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What is the expectation of rolling a fair 6-sided die?
💡 Hint: Consider how you can calculate the average of the sides.
True or False: Expectation can be calculated using both sums and integrals.
💡 Hint: Recall the different approaches to calculate expectation.
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Challenge Problems
Push your limits with advanced challenges
Given X is a normal random variable with mean = 10 and variance = 4, calculate E(X + 3).
💡 Hint: Use the linearity property of expectation.
Explain how expectation can simplify the analysis of a probability distribution in financial modeling.
💡 Hint: Think about the implications of average outcomes in risk assessment.
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Reference links
Supplementary resources to enhance your learning experience.