Create a **15-slide professional technical PPT** using the sources in this notebook for an internship qualification presentation at **Mistral Solutions**. Topic: **Probability, Statistics and Linear Algebra: Real-World Applications** The PPT should include: 1. **Introduction** to the three mathematical concepts and why they are important. 2. **Definitions and basic concepts** of Probability, Statistics, and Linear Algebra. 3. **Real-world applications** of all three, covering examples such as Digital Twins, Predictive Maintenance, Drones, Healthcare, Finance, Recommender Systems, BCI, NLP, Wearables, Fraud Detection, and Quantum Computing where supported by the sources. 4. A **comparison showing how Probability, Statistics, and Linear Algebra are used differently across applications**. 5. A detailed case study on **Digital Twin + Predictive Maintenance**. 6. Use one industrial machine example to demonstrate the mathematics: * Statistics: analyze historical sensor readings and detect anomalies. * Linear Algebra: represent sensor readings as a machine-state vector and calculate deviation from a healthy state. * Probability: estimate the probability/risk of machine failure using sensor evidence. 7. Show how the three mathematical concepts work together: **Sensor Data → Statistics → Linear Algebra → Probability → Digital Twin → Maintenance Decision** 8. End with the key takeaway that these mathematical foundations transform raw data into intelligent engineering decisions. ### Presentation requirements * Exactly **15 slides** * Professional technical style suitable for an internship evaluation * Definitions + applications + detailed case study * Use diagrams, tables, graphs, and simple mathematical examples * Keep slide text concise and avoid paragraphs * Include speaker notes for each slide * Use only information supported by the uploaded sources; clearly identify any illustrative numerical examples * Prioritize **understanding and practical application**, not just definitions