17.3 - Independence of Random Variables
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Practice Questions
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What is a random variable?
💡 Hint: Think of what you measure in experiments.
Can independent random variables affect each other's outcomes?
💡 Hint: Reflect on the concept of independence.
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Interactive Quizzes
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Two random variables are independent if:
💡 Hint: Recall the definition of independence.
If Cov(X, Y) = 0, then X and Y are definitely independent.
💡 Hint: Consider examples of uncorrelated but dependent variables.
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Challenge Problems
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Two people flip a coin simultaneously. Let A be the event of 'Person 1 gets heads' and B be 'Person 2 gets heads'. Are the events A and B independent? Justify your answer with probabilities.
💡 Hint: Consider the outcomes of independent events.
Given two dice rolls defined as random variables X and Y, show whether they are independent if the results are analyzed via conditional probabilities.
💡 Hint: Think about how the outcome of each die is calculated.
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