1. Unbiased

Thank you
Maria

2. you can prove that $E(S^2)=\sigma^2$ but you cannot pull the square root through the expectation.

I would just cook up an example and show that $E(S)\ne \sigma$

Try a bernoulli with P(X=0)=1-p and P(X=1)=p.
Here you have pq as the pop. variance.
Let n=3 and obtain the distribution of S and see what happens.

The sample of (0,0,0) occurs with probability q times q times q.
A sample of two 0's and one 1 occurs with probability pqq, but there are 3 of those....
So you can derive the distribution of S via these four possibilities.

3. Can you please show me how cause i can't understand?
Thank you

4. Originally Posted by maria69
Can you please show me how cause i can't understand?
Thank you
Please show some effort after getting help. What have you done and where do you get stuck?