Question

A={max(X,Y)=5} and B={min(X,Y)=3}

Answer 1

The events A and B, defined as
`\(A = \{\max(X, Y) = 5\}\)` and
`\(B = \{\min(X, Y) = 3\}\)`, respectively, represent the situations where the maximum of two random variables X and Y is 5 and the minimum is 3.

Step-by-step explanation:

In probability theory, events A and B are defined based on the random variables X and Y. Event A, denoted as
`\(A = \{\max(X, Y) = 5\}\)`, signifies the scenario where the maximum value between X and Y is 5. This occurs when either X or Y or both take the value of 5. Similarly, event B, denoted as
`\(B = \{\min(X, Y) = 3\}\)`, represents the situation where the minimum value between X and Y is 3. This occurs when either X or Y or both take the value of 3.

The events A and B are dependent on the specific values of X and Y, and the probability of each event occurring depends on the underlying distribution of X and Y. The interpretation of these events is essential in understanding the behavior of random variables in different scenarios.