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F07

Probability & Statistics

“Being clever about dice and coin flips”

Lessons

Start the course →0 of 20 lessons done
  1. Chance and frequencyFreeWhat does "a 1 in 6 chance" actually mean? You'll flip coins and roll dice thousands of times in a second, watch the results settle towards a fixed number, and learn the words every probability question is built from. Then you'll find the mistake that fooled a famous mathematician. · 14 min
  2. The rules of probabilityFreeRoll two dice. What's the chance of at least one six? Most people say 1 in 3, and they're wrong. You'll pick outcomes on a 36-square grid, discover the complement and union rules, and solve the gambling puzzle that started probability theory in 1654. · 15 min
  3. Conditional probabilityFreeNew information changes the odds. A friend peeks at two dice and says "there's at least one six". What's the chance of double six now? You'll watch the grid shrink as you learn things, discover why P(A given B) and P(B given A) can be wildly different, and build the rule behind every "people who bought this also bought" feature. · 15 min
  4. Independence🔒 MembersA coin lands heads three times in a row. Is tails now "due"? You'll test the gambler's fallacy with thousands of flips, learn what it really means for two events to be independent (and why that's not the same as "can't happen together"), and solve the birthday problem that surprises nearly everyone. · 15 min
  5. Bayes' rule🔒 MembersA test that's 90% accurate says you have a rare disease. What's the chance you really have it? Not 90%, and most doctors get this wrong. You'll see 1,000 people as colored squares, find the answer by counting, then learn Bayes' rule, the formula behind spam filters and much of machine learning. · 16 min
  6. Total probability and Monty Hall🔒 MembersThree doors, one car, two goats. You pick a door, the host opens another one to show a goat, and offers you a switch. Should you? This puzzle fooled thousands of people with PhDs. You'll play it, run it a few hundred times with a robot, and learn the tree method that settles it for good. · 16 min
  7. Random variables🔒 MembersUsually you don't care about the whole outcome, just one number from it, like the total on two dice. That number is a random variable, and its probabilities make a bar chart called a distribution. You'll predict the shapes, watch thousands of rolls fill them in, and code the PMF yourself. · 14 min
  8. Expected value🔒 MembersShould you pay $4 to play a dice game? Expected value answers it, and it's literally a balance point. You'll balance a seesaw of probabilities, discover why casinos always win in the long run, and use the most useful shortcut in probability, linearity of expectation, to solve a puzzle that looks impossible. · 15 min
  9. Variance and standard deviation🔒 MembersTwo pizza places both deliver in 30 minutes on average, but one is always within 2 minutes and the other can take 50. The average hides the difference; variance measures it. You'll stretch and squeeze a distribution on the seesaw, compute spread by hand and in code, and see why rolling two dice is safer than doubling one. · 15 min
  10. The binomial distribution🔒 MembersYou guess every answer on a 10-question multiple-choice quiz. What's the chance you pass? Drop balls through a board of pegs, watch a famous shape appear, and learn the formula that counts successes in repeated tries, the binomial distribution, along with its mean and spread. · 16 min
  11. Waiting times: the geometric distribution🔒 MembersA rare item drops 5% of the time. How many tries until you get it? On average 20, but more than a third of players will need longer, and bad luck so far doesn't make it come any sooner. You'll explore the distribution of waiting times, prove the "1 over p" rule, and work out how long it takes to collect a full set of stickers. · 15 min
  12. Rare events: the Poisson distribution🔒 MembersA help desk gets 3 tickets an hour on average. How often is an hour completely quiet? How often is it a flood? Counts of random, independent events follow one distribution, the Poisson. You'll see it appear as the limit of the binomial, then test it on a famous 1898 data set about soldiers kicked by horses. · 15 min
  13. Continuous random variables🔒 MembersA bus comes every 10 minutes and you arrive at a random moment. What's the chance you wait exactly 3 minutes? Zero! When a quantity can be any number, probability becomes area under a curve. You'll shade areas, meet the uniform and exponential distributions, and learn how computers turn random.random() into any distribution you like. · 15 min
  14. The normal distribution🔒 MembersThe bell curve shows up in test scores, measurement errors and the Galton board. You'll shade areas under it to discover the 68–95–99.7 rule, turn any value into a z-score that says "how unusual is this?", and use Python's NormalDist to answer real questions, including how well the bell curve approximates coin flips. · 16 min
  15. Law of large numbers and the central limit theorem🔒 MembersWhy does the bell curve show up everywhere? Because averages of almost anything turn into bells. You'll take thousands of samples from lopsided, two-humped and coin-flip populations and watch their averages line up into a narrow bell every time. Then you'll use the √n rule to estimate π by throwing random darts. · 17 min
  16. Estimation🔒 MembersSo far you've known the true probabilities and predicted the data. Statistics flips that around. You see some data and estimate the truth. You'll discover why sample variance divides by n − 1, measure how far off an estimate typically is, and use the trick Allied statisticians used in World War II to count enemy tanks from a handful of serial numbers. · 16 min
  17. Confidence intervals🔒 MembersA poll says "52% support, plus or minus 3 points, with 95% confidence." What does that really promise? You'll draw hundreds of intervals from a machine whose true average you secretly know, count how many catch it, and learn exactly what "95% confident" means, what makes an interval wider or narrower, and what it can't protect you from. · 16 min
  18. Hypothesis tests and p-values🔒 MembersA coin lands heads 60 times out of 100. Is it rigged, or just lucky? Hypothesis testing answers "could chance alone explain this?" You'll simulate thousands of fair coins to compute a p-value by hand, find the line between "surprising" and "not", and learn how A/B tests work and how p-hacking fools people. · 17 min
  19. Correlation🔒 MembersIce cream sales and drownings rise and fall together. Does ice cream cause drowning? You'll learn to measure how strongly two things move together, train your eye with a guess-the-correlation game, and meet Simpson's paradox, where a trend reverses when you split the data into groups. · 16 min
  20. Boss level: a Naive Bayes spam filter🔒 MembersPut the whole course to work. You'll build the same kind of spam filter that rescued email inboxes in the early 2000s, from nothing but counting words and Bayes' rule. Train it on example messages, fix the two problems that break the simple version (zero counts and vanishing numbers), and measure how accurate it is on mail it has never seen. · 22 min

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