A variable, x, is uniformly distributed between 0 and 3,600. In a random sample of n = 60, if x̄ represents the variable's sample mean, what is E(x̄)?

Question

A variable, x, is uniformly distributed between 0 and 3,600. In a random sample of n = 60, if x̄ represents the variable's sample mean, what is E(x̄)?

I am having trouble understanding what the question is asking.

Answer 1

E(X) is the expected value, which is typically going to be the population mean. In a uniform distribution, the (population) mean, or expected value, is very much what you would expect a mean to look like: the average of the boundary values. This is (0 + 3600) / 2 = 1800.

The question is asking what the expected value of the mean is. This is actually a very easy question. It's exactly the same as the mean that you already have. One of the properties of the expected value is that E(A) = A, where A is some constant value. In other words, if A was equal to 5, then would say that we expect 5 to be 5. So, E(E(X)) = E(X). In English, we expect the expected value to be the expected value (did I say "expected" enough times?).

In the case of the mean, the sample size is irrelevant. The standard deviation (which we're not finding here), does change depending on the sample size. In any case, E(x̄) = x̄ = 1800.