Probability and Statistics for ML Careers

Start by distinguishing an observed quantity from the population or process you want to understand. A sample mean describes the records collected, but a biased sampling process can make it misleading for a wider population. Inspect missing observations, repeated entities and how examples were selected. More rows do not automatically repair selection bias or make dependent observations independent. Learn distributions and summaries together. For the illustrative values [0, 0, 0, 20], the mean is 5 while the median is 0. Neither number is inherently wrong; each answers a different question about the data. Examine spread and unusual values before presenting one average as a complete description. Conditional probability changes the group under consideration. The fraction of true events among alerts is different from the fraction of all true events that were alerted. Suppose a toy dataset contains 1,000 cases, including 10 true events. A system flags all 10 events and 90 other cases. Its alert precision is 10 divided by 100, or 10%; its recall is 10 divided by 10, or 100%. These invented counts show why high recall can coexist with many false alerts. Uncertainty estimates depend on assumptions and the evaluation design. In the usual frequentist interpretation, a 95% confidence procedure covers a fixed population parameter in 95% of repeated samples under its assumptions; it does not promise that every resulting interval contains the truth. Keep final test data separate from repeated tuning and inspect important groups as well as averages. Prediction also differs from causation: an association alone does not show what would happen if someone changed an input.