17.6 - Why Independence Matters in PDEs
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Practice Questions
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What is the definition of independence in random variables?
💡 Hint: Think about the relationship between probabilities.
Give an example of independent random variables in real life.
💡 Hint: Consider scenarios where one event does not influence the other.
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Interactive Quizzes
Quick quizzes to reinforce your learning
If P(X=x, Y=y) = P(X=x) * P(Y=y), what can we say about X and Y?
💡 Hint: Consider the implications of the joint probability.
True or False: Independence of random variables means that their expected values can be treated independently.
💡 Hint: Think about how expected values are combined for independent variables.
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Challenge Problems
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Consider two continuous random variables X and Y with joint PDF f(x, y) = e^(-x) * e^(-y). Verify if they are independent.
💡 Hint: Look closely how you can factor the joint PDF.
In a certain communication system, noise variables N1 and N2 are modeled as independent. If both have a mean of 0 and variance of 1, what can be said about their influence on the total noise N = N1 + N2?
💡 Hint: Remember the properties of independent random variables.
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