Introduction
When preparing for the Mathematics Optional subject in UPSC, it is important to have a clear understanding of mathematical statistics and hypothesis testing. Both concepts are interrelated and often go hand in hand. However, whether to revise them separately or together depends on various factors.

Revising Concepts Separately

Advantages:
1. In-depth understanding: By revising mathematical statistics and hypothesis testing separately, you can focus on each concept individually, allowing for a more detailed understanding of both.
2. Clear conceptual clarity: Separating the revision of these concepts can help you develop a clear understanding of the underlying principles, theories, and formulas associated with each.
3. Better time management: If you have limited time for revision, separating the concepts can help you allocate specific time for each, ensuring that you cover all the important topics thoroughly.

Disadvantages:
1. Limited perspective: By revising these concepts separately, you might miss out on the interconnections between them. Understanding the relationship between statistical concepts and hypothesis testing is crucial for comprehensive knowledge.
2. Difficulty in application: Mathematical statistics and hypothesis testing are often applied together in real-world scenarios. By revising them separately, you might find it challenging to apply the concepts effectively when solving complex problems.

Revising Concepts Together

Advantages:
1. Holistic understanding: By revising mathematical statistics and hypothesis testing together, you can develop a holistic understanding of how these concepts are interrelated and how they complement each other.
2. Practical application: By studying both concepts simultaneously, you will be better equipped to apply statistical methods and hypothesis testing techniques in real-world scenarios, enabling you to solve problems more effectively.
3. Comprehensive coverage: Revising these concepts together ensures that you cover all the relevant topics and concepts required for a thorough understanding of mathematical statistics and hypothesis testing.

Disadvantages:
1. Time management challenge: Combining the revision of mathematical statistics and hypothesis testing requires efficient time management. It can be challenging to allocate sufficient time to cover all the topics thoroughly.
2. Overwhelming complexity: If you are not familiar with the basics of these concepts, studying them together might be overwhelming and confusing. It is important to have a strong foundation before attempting to integrate the two.

Conclusion
In conclusion, the decision to revise mathematical statistics and hypothesis testing separately or together depends on various factors such as time availability, prior knowledge, and personal learning preferences. It is recommended to have a basic understanding of both concepts before attempting to integrate them. Ultimately, a comprehensive understanding of the interconnections between mathematical statistics and hypothesis testing is crucial for success in the Mathematics Optional subject for UPSC.