Statistical Definitions and Statement: X, S^2, μ, σ^2, True or False

[lina29]

Homework Statement

Let X1,…,Xn denote a random sample from a population with mean μ and variance σ^2. Assume that both μ and σ^2 are finite but unknown. Let X denote the sample mean and S^2 denote the sample variance. Are the following statements true or false?
A-There is no difference between X and μ - the two are different notations for the same quantity.
B- There is no difference between S^2 and σ^2 - the two are different notations for the same quantity.
C- X is an unbiased estimator for μ.
D- The standard error of X is σ/(sqrt n) which can be estimated as S/sqrt(n).

Homework Equations

The Attempt at a Solution

I believe I have the right answers I just want to double check
A- yes
B- yes
C- yes
D- no

 

[Bacle2]

Actually, as I understood, a),b) are false. If they were equal, confidence intervals would not be necessary. For c),d) , there are actual formulas, so that you can verify.

 

[lina29]

Thank you!