Developing a strong foundation in mathematical statistics for Paper I is essential for success in the UPSC exam. Here are some detailed steps to help you in this process:

1. Understand the Basics:
- Start by understanding the basic concepts of mathematical statistics, such as probability, random variables, and distributions.
- Familiarize yourself with key terms and definitions, such as mean, variance, standard deviation, and correlation.
- Learn about different types of distributions, including the normal distribution, binomial distribution, and Poisson distribution.

2. Study Probability Theory:
- Probability theory forms the basis of mathematical statistics. Study topics like sample spaces, events, probability laws, and conditional probability.
- Learn about important concepts like independence, random variables, and joint probability distributions.
- Practice solving problems involving probability, such as calculating probabilities of events and finding expected values.

3. Learn Statistical Inference:
- Statistical inference deals with drawing conclusions and making predictions based on data. Study topics like estimation and hypothesis testing.
- Understand different estimation techniques, including point estimation and interval estimation.
- Learn about hypothesis testing, including null and alternative hypotheses, test statistics, p-values, and type I and type II errors.

4. Master Sampling Techniques:
- Sampling techniques are crucial in statistical analysis. Study different sampling methods, such as simple random sampling, stratified sampling, and cluster sampling.
- Understand the importance of sampling distribution and the central limit theorem.
- Practice solving problems related to sampling techniques and estimating population parameters.

5. Gain Practical Experience:
- Apply your knowledge by solving practice problems and numerical exercises from textbooks and previous years' question papers.
- Use statistical software like R or Python to analyze data and perform statistical tests.
- Review and analyze real-life examples and case studies to understand the application of mathematical statistics in various fields.

6. Practice Mock Tests:
- Regularly attempt mock tests and previous years' question papers to assess your understanding and identify areas of improvement.
- Analyze your performance and focus on areas where you need more practice.
- Time yourself during these tests to improve your speed and accuracy.

Remember, consistent practice and revision are key to developing a strong foundation in mathematical statistics for Paper I. Stay focused, manage your time effectively, and seek clarification whenever needed. Good luck!