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"Mutually independent" random variables refer to a set of variables in a probability distribution that are not influenced by each other. In other words, the occurrence of one variable does not affect the probability of the other variables occurring.
To determine if two random variables are mutually independent, you can use the definition of independence: if the joint probability of the two variables is equal to the product of their individual probabilities, then they are considered mutually independent.
Yes, three or more random variables can be mutually independent. The same definition of independence applies: the joint probability of all variables must be equal to the product of their individual probabilities.
The significance of having mutually independent random variables is that it simplifies probability calculations. When variables are independent, the probability of one event occurring does not affect the probability of another event occurring, making it easier to calculate probabilities and make predictions.
Yes, it is possible for two random variables to be independent but not mutually independent. This occurs when the joint probability of the variables is equal to the product of their individual probabilities, but the variables are not independent when combined with a third variable. In this case, the variables are considered to be conditionally independent.
