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2 cards from this section. Quick, good the night before a test.
Define independence of random variables.
Think about how one variable's outcome impacts another.
Given P(X=2) = 0.3, P(Y=3) = 0.5, calculate P(X=2, Y=3) if X and Y are independent.
Use the formula for the joint probability of independent events.
What is the definition of independence in probability?
Consider the influence one variable has over another.
If P(X=1) = 0.4 and P(Y=2) = 0.6, what is P(X=1, Y=2) if X and Y are independent?
Multiply the individual probabilities of X and Y.
A fair die is rolled twice. What is the probability of rolling a two on the first roll and a three on the second? Are these events independent?
Use the independence formula for joint probabilities.
If X and Y are independent random variables with P(X=1) = 0.2 and P(Y=1) = 0.5, what is P(X=1, Y=1)? Are they independent?
Apply the independence condition to find joint probabilities.
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