Stats question, how to get expected values

[wtmoore]

Homework Statement

I have taken a random sample such that X~N(8,2).

I want to use the samples that I have generated to estimate E(xbar), E(s²), E(α²₁) and E(α²₂) for the population.

Homework Equations

The Attempt at a Solution

I am not entirely sure how to do these.

I know that for a random variable, E(x)= (x1 + x2 ... +xn)/n, but I am not sure if this is the same for a sample/xbar.

I have googled and can't find the formulas, does anyone know them here?

I know for s^2 that E(s^2) = E[{sum(i to n) (xi-xbar)^2}/(n-1)]

so now I can bring the 1/(n-1) out front of the E, but I'm not sure how the summation acts.

 

[sunjin09]

You are confusing some concepts. You want to estimate say, the mean of the random variable X μ=E{X}, you use the estimator \bar{x}=\frac{1}{N}\sum_nx_n where x_n are the samples of X. You can prove E[\bar{x}]=\mu so that the estimator which is a function of the samples has an expected value that is equal to the mean μ of X, so that this estimator is unbiased. Now try to find unbiased estimators of other parameters of the random variable X that you want to estimate, as a function of the samples, i.e., the expected values are equal to the parameters you want to estimate.