From the AM-GM inequality, we know that the arithmetic mean (AM) of a list of non-negative real numbers is always greater than or equal to the geometric mean (GM). But the inequality doesn't tell us just how much larger the AM is.
Given a list of random real numbers chosen uniformly and independently in the range where find in terms of
Then find .
If the formula is of the form where are positive integers, give your answer as
Note: The notation is the expected value of the random variable