Minimum and maximum of random variables

1. How do you find the maximum of a random variable?
2. Are Max and Min of random variables independent?
3. What is the range of random variable?
4. What are the two requirements for a random variable?

How do you find the maximum of a random variable?

The maximum of a set of IID random variables when appropriately normalized will generally converge to one of the three extreme value types. This is Gnedenko's theorem,the equivalence of the central limit theorem for extremes. The particular type depends on the tail behavior of the population distribution.

Are Max and Min of random variables independent?

The min and max are a function of independent random variables, yet they have covariance. The min and the max cannot be independent.

What is the range of random variable?

The range of a random variable X, shown by Range(X) or RX, is the set of possible values for X. In the above example, Range(X)=RX=0,1,2,3,4,5. The range of a random variable X, shown by Range(X) or RX, is the set of possible values of X.

What are the two requirements for a random variable?

In the development of the probability function for a discrete random variable, two conditions must be satisfied: (1) f(x) must be nonnegative for each value of the random variable, and (2) the sum of the probabilities for each value of the random variable must equal one.