Let Xnn ge 1 be a sequence of random variables having the following probability mass function P(Xn = x) = 1/5n(1 - 1/5n)^x, x = 0, 1, 2, dots; n in N. Define Zn = Xn/n, n in N, and let V be a random variable. If Zn xrightarrowd V, as n to infty, then which of the following statements is/are correct?

Q53Section ST (Statistics (Q11–Q65))53 of 65

Geometric scaling limit

Let $\{X_n\}_{n \ge 1}$ be a sequence of random variables having the following probability mass function $P(X_n = x) = \frac{1}{5n}\left(1 - \frac{1}{5n}\right)^x$ , $x = 0, 1, 2, \dots$ ; $n \in \mathbb{N}$ . Define $Z_n = X_n/n$ , $n \in \mathbb{N}$ , and let $V$ be a random variable. If $Z_n \xrightarrow{d} V$ , as $n \to \infty$ , then which of the following statements is/are 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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