请问MUD怎么可能同时发生呢？

问题如下：

A research analyst at a boutique investment firm is assessing the impact of an increase in short-term interest rates on the credit rating of bank MSC. The analyst identifies all possible outcomes for the scenario and notes that the rating of bank MSC can either be maintained at the same level (M), be upgraded (U), or be downgraded (D). Which of the following correctly describes the event space?

选项：

A.The event space consists of four events. B.The event space can be represented by the following set: {M, U, D, {M,U}, {M,D}, {U,D}, {M,U,D}, Ø}, where Ø is the empty set. C.The event space in this scenario is a continuous probability space. D. The event space is identical to the sample space of the scenario.

解释：

B is correct. The event space consists of all combinations of outcomes to which probabilities can be assigned. In this scenario, {M}, {U}, and {D} are the possible outcomes of the experiment. The event space can therefore be described as containing the following events:

1. M occurs, U and D do not occur
2. U occurs, M and D do not occur
3. D occurs, M and U do not occur
4. M and U occur, D does not occur
5. M and D occur, U does not occur
6. U and D occur, M does not occur
7. M, U and D occur
8. Neither M, U, nor D occur (empty set)

This would give an event space consisting of 8 events: {M, U, D, {M,U},{MD},{M,D},{M,U,D}, Empty Set}.

Note that a definite probability of 0 can be assigned to the “impossible” events, which are events 4,5,6,7, and 8.

A is incorrect. As explained above, the event space consists of 8 events.

C is incorrect. Because the event space has a finite number of outcomes, it is called a discrete probability space.

D is incorrect. The sample space is the set containing all possible outcomes of an experiment. We know that the outcome can only be one of the 3, which gives us a sample space of {M, U, D}.

Learning Objective: Describe an event and an event space.

Reference: Global Association of Risk Professionals. Quantitative Analysis. New York, NY: Pearson, 2023, Chapter 1, Fundamentals of Probability [QA-1].