# Math Help - Bias

1. ## Bias

Suppose that X1, X2,...Xn is a random sample size n from a normal distribution
N(0, theta) with mean 0 and variance theta.

State which of these estimators, theta 1, 2 and 3 are biased, giving the bias if so. If not then give a justification

theta 1 = $\sum \frac{X^2}{(n-1)}$
theta 2 = $\sum \frac{X^2}{n}$
theta 3 = $nXbar^2$

Please just help me with a way into this question, a starting point, since I am clueless. A method to approach it and I will do all calculations. I know what a bias is but I don't know how to approach it. Find the real variance and equate? I am not sure. Thanks

any ideas?

3. ## Re: Bias

In the first part, for example, you simply need to find the expected value of
$\sum \frac{X^2}{n-1}$.

Hint: You might find knowledge of the chi squared distribution useful (although that's not the only way).