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Answer: The event space can be represented by the following set: {M, U, D, {M,U}, {M,D}, {U,D}, {M,U,D}, ∅}, where ∅ is the empty set.
## Explanation **B is correct** because the event space consists of all possible combinations of outcomes to which probabilities can be assigned. In this scenario with three possible outcomes (M, U, D), the event space contains all subsets of the sample space: - **Individual outcomes**: {M}, {U}, {D} - **Pairs of outcomes**: {M,U}, {M,D}, {U,D} - **All three outcomes**: {M,U,D} - **Empty set**: ∅ This gives us 2³ = 8 events in total. **Why other options are incorrect:** - **A is incorrect** because the event space consists of 8 events, not 4. - **C is incorrect** because with a finite number of discrete outcomes, this is a discrete probability space, not a continuous one. - **D is incorrect** because the sample space is {M, U, D} (only the three basic outcomes), while the event space includes all combinations and subsets of these outcomes. **Key Concepts:** - **Sample Space**: The set of all possible elementary outcomes {M, U, D} - **Event Space**: The power set of the sample space, containing all possible combinations of outcomes - **Discrete vs Continuous**: Finite outcomes make this a discrete probability space
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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?
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}, ∅}, where ∅ 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.
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