Let Omega = 1,2,3,… and H be the collection of all subsets of Omega. Let P be a probability measure on H such that P(k) = 1/2^k, k ge 1. Further, let X: Omega to R be defined by X(omega) = omega for all omega in Omega. Then which of the following statements is/are true?

Q50Section ST (Statistics (Q11–Q65))50 of 65

Tail limits of a dyadic distribution

Let $\Omega = \{1,2,3,…\}$ and $\mathcal{H}$ be the collection of all subsets of $\Omega$ . Let $P$ be a probability measure on $\mathcal{H}$ such that $P(\{k\}) = \frac{1}{2^k}$ , $k \ge 1$ . Further, let $X: \Omega \to \mathbb{R}$ be defined by $X(\omega) = \omega$ for all $\omega \in \Omega$ . 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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