Question
You are trying to prove that a sequence of random variables converges to a limit, so you get one of these functions out of the Skorokhod space that you keep in your backpack. For 10 points each:
[10e] You first try to show convergence of these functions, which is called “weak convergence.” These functions can be calculated by taking the integral of a probability density function.
ANSWER: cumulative distribution functions [or CDFs; prompt on distribution functions]
[10m] To prove convergence in probability, you apply this statement that places an upper bound of “expectation of X over c” on the probability of a positive random variable X exceeding a constant c.
ANSWER: Markov’s inequality
[10h] If the event that X sub n is more than epsilon away from X has summable probability for any epsilon, then you can apply the first of these statements to get almost sure convergence. Both of these statements concern the probability of the limit supremum of a sequence of events.
ANSWER: Borel–Cantelli lemmas
<Tim Morrison, Other Science - Mathematics>
Summary
| 2023 Chicago Open | 08/05/2023 | Y | 9 | 12.22 | 78% | 33% | 11% |
Data
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