Existence of a Non-negative Integrable Random Variable with Supremum-Constrained Survival Function
Let $( X_1,\dots,X_n,\dots )$ be a sequence of non-negative integrable random variables, Denote by $S_i(t) = \mathbb{P}(X_i \geq t)$, the survival function of $X_i, i \ge 1$
Does there exist a non-negative and integrable random variable X with survival function S, such that $ \sup_nS_n(t) \leq S(t), \, \forall t \ge 0$?
36
Answer
Answers can only be viewed under the following conditions:
- The questioner was satisfied with and accepted the answer, or
- The answer was evaluated as being 100% correct by the judge.

4.8K
The answer is accepted.
Join Matchmaticians Affiliate Marketing
Program to earn up to a 50% commission on every question that your affiliated users ask or answer.
- answered
- 373 views
- $20.00
Related Questions
- A problem on almost singular measures in real analysis
- What Are The Odds ?
- Operational Research probabilistic models
- Product of Numbers from a Log Normal Distribution
- Number of different drinks that can be made using 6 ingredients
- Correlation of Normal Random Variables
- Find Mean, Variance, and Distribution of Recursively Defined Sequence of Random Variables
- Geometric distribution