For nge 2, let X1,X2,…,Xn be a random sample from a distribution with E(X1)=0, Var(X1)=1 and E(X1^4)<infty. Let bar Xn=frac1nsumi=1^n Xiquadandquad Sn^2=frac1n-1sumi=1^n(Xi-bar Xn)^2. Then which of the following statements is/are always correct?

Q38Section B (Section B)38 of 60

Always-true properties of sample mean and variance

For $n\ge 2$ , let $X_1,X_2,…,X_n$ be a random sample from a distribution with $E(X_1)=0$ , $\mathrm{Var}(X_1)=1$ and $E(X_1^4)<\infty$ . Let $\bar X_n=\frac1n\sum_{i=1}^n X_i\quad\text{and}\quad S_n^2=\frac1{n-1}\sum_{i=1}^n(X_i-\bar X_n)^2.$ Then which of the following statements is/are always correct?

Multiple select: one or more options are correct. Select all of them, then submit — marks need the exact set.

Select every correct option, then submit.

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