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2 cards from this section. Quick, good the night before a test.
What is the definition of independence in random variables?
Think about the relationship between probabilities.
Give an example of independent random variables in real life.
Consider scenarios where one event does not influence the other.
If P(X=x, Y=y) = P(X=x) * P(Y=y), what can we say about X and Y?
Consider the implications of the joint probability.
True or False: Independence of random variables means that their expected values can be treated independently.
Think about how expected values are combined for independent variables.
Consider two continuous random variables X and Y with joint PDF f(x, y) = e^(-x) * e^(-y). Verify if they are independent.
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?
Remember the properties of independent random variables.
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