CSIR NET Maths previous year question papers

Multi-select · full marks only for the exact set · Limit Theorems and Markov Chains

1. A

   $X_{n}$ converges to X almost surely as $n \to \infty$ implies that $X_{n}$ converges to X in probability as $n \to \infty$.

2. B

   $X_{n}$ converges to X in probability as $n \to \infty$ implies that $X_{n}$ converges to X almost surely as $n \to \infty$.

3. C

   If $\sum(n=1..\infty)$ ℙ[|$X_{n} - X$| $> \delta] < \infty$ for all $\delta > 0$, then $X_{n}$ converges to X almost surely as $n \to \infty$.

4. D

   If $X_{n}$ converges to X in distribution as $n \to \infty$, and X is a constant with probability 1, then $X_{n}$ converges to X in probability as $n \to \infty$.