Let Xnnge 1 be a sequence of random variables, where XnsimBin(n,pn) with pnin(0,1). Which of the following conditions implies that Xnxrightarrowd0 as ntoinfty?

Q30Section A (Section A)30 of 60

A condition for binomials to go to zero

Let $\{X_n\}_{n\ge 1}$ be a sequence of random variables, where $X_n\sim\mathrm{Bin}(n,p_n)$ with $p_n\in(0,1)$ . Which of the following conditions implies that $X_n\xrightarrow{d}0$ as $n\to\infty$ ?

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