Topics
14 topics, each building on the one before.
- 1Data and samplingStatistics is using data to make a decision. You can't check everyone, so you check a slice (the sample) and let it speak for the whole group (the population).
- 2Where is the middleMean is the average. Median is the middle once sorted. Mode is the most common. The big idea: one extreme number drags the mean; the median barely moves.
- 3How spread out is itRange is biggest minus smallest. Standard deviation is the typical distance from the average; in finance, risk. Empirical rule: on hill-shaped data, 68% fall within 1 SD, 95% within 2.
- 4Probability rulesOr: add, then subtract the overlap. And: multiply. Given: count only inside what you were told. Mutually exclusive: can't both happen. Independent: one says nothing about the other.
- 5Random variablesA random variable is a number that depends on chance. Its expected value is the long-run average, weighted by probability. Its SD is the risk around that.
- 6Two variables and portfoliosCovariance asks whether two things move together. Correlation rescales it from −1 to +1. Mix two assets and any correlation below +1 lowers the mix's risk. That is diversification.
- 7Counting and the binomialRepeat a yes-or-no try n times with the same chance p: the count of yeses is binomial, mean np, variance np(1 − p). Combinations count the ways it can happen.
- 8PoissonPoisson counts events in a fixed window when they arrive at a steady average rate λ. Mean and variance both equal λ. Scale λ to the window first.
- 9The normal curveThe normal is the bell. Measure in SDs from the mean, z = (y − μ) / σ, and any normal becomes the standard one. Area under it is probability.
- 10Sampling and the CLTSample means have their own distribution. The Central Limit Theorem says it is near normal for big n, centered on μ, with spread σ / √n (the standard error).
- 11Confidence intervalsA confidence interval is your estimate plus or minus a margin: estimate ± critical value × standard error. Use z when σ is known, t when you only have s.
- 12Hypothesis testsA hypothesis test asks: would this data be surprising if nothing were going on? Assume nothing is (H₀). A small p-value means the data would be rare, so reject H₀.
- 13Simple regressionRegression fits the line with the smallest squared misses. Slope: how much y moves per unit of x. R²: the share of y's variation explained. t-test: does x help?
- 14Multiple regressionSeveral x's. Each coefficient is one x's effect holding the others fixed. The F-test checks the whole model, each t-test one x. Multicollinearity: two x's saying the same thing.