Topic 2: Expected Value & Variance

Let’s be real, once you move past simple averages and start doing Variance and Covariance, things get messy! I wrote these notes to keep my head straight, and they’ve been a lifesaver for my revision. I’ve tried to make the math look a lot less scary and a lot more logical. Everything inside my notes: 1. Expected Value Essentials: Detailed definitions for both Discrete and Continuous random variables, including the sum and integral formulas for calculating the mean. 2. Variance and Standard Deviation: Step-by-step guides on measuring the spread of data, featuring the specific formulas for both discrete and continuous outcomes. 3. The Law of the Unconscious Statistician (LOTUS): Clear explanations for finding the expectation of a function of a random variable, which is essential for solving more advanced probability problems. 4. Linear Combinations and Rules: A handy reference for the rules of expectation and variance, including how to handle constants and linear transformations like aX + b. 5. Joint Distributions and Covariance: In-depth coverage of Covariance and Correlation, explaining how to determine and measure the linear relationship between two different random variables. 6. Practical Sample Statistics: Includes the essential formulas for calculating Sample Mean, Sample Variance, and the Sample Correlation Coefficient from real-world data pairs.