Variance of bootstrap sample of size n

[ghostyc]

http://img138.imageshack.us/img138/6060/98259799.jpg

I have done part one and found that the bias is $$\frac{\theta}{n}$$

then i don't know how to proceed.

in my notes, have the following result,

http://img189.imageshack.us/img189/9699/resultc.jpg

i am thinking, this time i have to find the bias in $$\hat{\theta^*}$$
then, if i work through, i got it's unbiased...

am i doing something wrong?

I am confused with that, the result in my notes, is it for the mean of the sample?

but here, we are aksed for the population variance?

Thanks

 

[EnumaElish]

(ii) is asking about theta star HAT, not theta star BAR.

 

[ghostyc]

(ii) is asking about theta star HAT, not theta star BAR.

i will look into it again
sometimes, i really get confused what i am looking for

 

[ghostyc]

(ii) is asking about theta star HAT, not theta star BAR.

I am now working on the bias is

$$\bar{\theta}^{*} - \hat{\theta} = \frac{1}{n} \sum_{i=1}^n (y_i^* - \bar{y} )^2 - \frac{1}{n} \sum_{i=1}^n (y_i - \bar{y} )^2$$
after some munipulation , i got to

$$<br /> \frac{1}{n} \sum_{i=1}^n \left( {y_i^*}^2 - y_i^2 -2\bar{y} (y_i^*+y_i) \right)<br />$$

then i take expectation, i got stuck again...