Unit 7 Summary

Math for CS · Axiom Academy

Complete review of all probability concepts Probability theory gives us a formal framework for reasoning about uncertainty. Every concept we covered builds on a few core ideas. The sample space is the set of all possible outcomes. An event is any subset. Counting underpins probability in finite sample spaces. Know when to use each tool. Conditional Probability & Independence Two events are independent when knowing one tells you nothing about the other: The crown jewel of conditional probability. It lets us reverse the direction of conditioning: Random Variables & Expectation A random variable assigns a number to each outcome. Works even when X, Y are not independent. Single trial, success probability p . E[X] = p , n independent trials. E[X] = np Trials until first success. P(X=k) = (1-p)^ k-1 p E[X] = 1/p Rare events in fixed interval. These bound how far a random variable can stray from its mean. Hashing: Birthday paradox gives collision probability Randomized algorithms: Expected runtime of randomized quicksort is Naive Bayes classifiers: Apply Bayes' theorem with independence assumption for fast text classification Networking: Packet loss and retransmission modeled by geometric distribution Load balancing: Balls-into-bins analysis uses Chernoff bounds Machine learning: MLE, MAP estimation, and Bayesian inference all rest on conditional probability Axiom Academy | Probability for Computer Science

This is the written version of the interactive lesson above. See the full Math for CS course.