Let Xnnge 1 be a sequence of i.i.d. random variables such that P(X1=0)=1/4=1-P(X1=1). Define Un=1/nsumi=1^nXiquadandquad Vn=1/nsumi=1^n(1-Xi)^2,quad n=1,2,… Then which of the following statements is/are TRUE?

Q38Section B (Section B)38 of 60

Laws of large numbers for indicators

Let $\{X_{n}\}_{n\ge 1}$ be a sequence of i.i.d. random variables such that $P(X_{1}=0)=\dfrac{1}{4}=1-P(X_{1}=1)$ . Define $U_{n}=\frac{1}{n}\sum_{i=1}^{n}X_{i}\quad\text{and}\quad V_{n}=\frac{1}{n}\sum_{i=1}^{n}(1-X_{i})^{2},\quad n=1,2,…$ 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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