Minimum of two random variables

1. What is the max of two random variables?
2. What is the expected value of the minimum of two uniform random variables?
3. Are Max and Min of random variables independent?
4. What is the minimum of a distribution?

What is the max of two random variables?

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.

What is the expected value of the minimum of two uniform random variables?

we get E[T]=1n+1. Notice that as n→∞ the expected value of the minimum of these uniform random variables goes to zero. In addition, this expectation is always in (0,1/2] for n≥1.

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 minimum of a distribution?

Your required minimum distribution is the minimum amount you must withdraw from your account each year. You generally have to start taking withdrawals from your IRA, SEP IRA, SIMPLE IRA, or retirement plan account when you reach age 72 (70 ½ if you reach 70 ½ before January 1, 2020).