
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 = $\displaystyle \sum \frac{X^2}{(n1)}$
theta 2 = $\displaystyle \sum \frac{X^2}{n}$
theta 3 = $\displaystyle nXbar^2$
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

Re: Bias

Re: Bias
In the first part, for example, you simply need to find the expected value of
$\displaystyle \sum \frac{X^2}{n1}$.
Hint: You might find knowledge of the chi squared distribution useful (although that's not the only way).