Let X1,X2,…,Xn be i.i.d. Poisson(lambda) random variables, where lambda0. Define barX=1/nsumi=1^nXiquadandquad S^2=1/n-1sumi=1^n(Xi-barX)^2 Then which of the following statements is/are TRUE?

Q39Section B (Section B)39 of 60

Sample mean beats sample variance for Poisson

Let $X_{1},X_{2},…,X_{n}$ be i.i.d. $\mathrm{Poisson}(\lambda)$ random variables, where $\lambda>0$ . Define $\bar{X}=\frac{1}{n}\sum_{i=1}^{n}X_{i}\quad\text{and}\quad S^{2}=\frac{1}{n-1}\sum_{i=1}^{n}(X_{i}-\bar{X})^{2}$ Then which of the following statements is/are TRUE?

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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