- High school๐ฒProbability๐
Variance and standard deviation: dispersion in 2 formulas
How to measure a data set's spread. Variance = mean squared deviation. Standard deviation = square root of variance.
- High school๐ฒProbability๐ณ
Probability tree: the 3 rules to compute a probability without mistakes
Along a branch you multiply, on the outcomes you add, siblings sum to 1. Three rules, that's it.
- High school๐ฒProbability๐
Normal distribution N(ฮผ, ฯยฒ): the bell curve and exam probabilities
Mean ฮผ = center, standard deviation ฯ = width. The 68-95-99.7 rule and how to compute probabilities on a calculator.
- High school๐ฒProbability๐
Mean, median, quartiles: who finds what, how
Three location indicators, three ways to summarize a data set. Don't mix them up; know when to use each.
- High school๐ฒProbability๐ฒ
Law of total probability: partition to count
P(A) = ฮฃP(A โฉ B_i) = ฮฃP(A|B_i)ยทP(B_i). Decompose over a partition.
- High school๐ฒProbability๐ฏ
Conditional probability: $P(A|B)$ without getting it wrong
ยซ Probability of A **given** B ยป. Simple formula, but 90% of errors come from picking the wrong universe. Here's how never to slip.
- High school๐ฒProbability๐ฏ
Expectation of binomial: E(X) = np, V(X) = np(1โp)
Over n trials with success probability p, expect np successes. Two formulas, one intuition.
- High school๐ฒProbability๐
The birthday paradox: how many people until two share a birthday?
365 days, but only 23 people are enough for the probability to exceed 50%. One of the most counter-intuitive results in probability.
- High school๐ฒProbability๐ฒ
Binomial distribution: the formula you need for exams
n trials, probability p, we want k successes. The formula + three conditions to check + calculator use.
- High school๐ฒProbability๐งฎ
Binomial coefficient C(n,k) = n! / (k!(nโk)!)
Number of ways to choose k out of n. Pascal's triangle computes it without factorials.