ManiMage.ai

Statistics

Probability, counting, distributions, expected value and spread, Bayes' rule, the law of large numbers, the normal curve and sampling.

10 stops21 min

Start withProbability2:23 See it on the map

The lessons, in order

  1. Probability

    measuring maybe

    Chance becomes a number between 0 and 1 — and suddenly you can do arithmetic with maybe.

    2min2:23

  2. Counting the ways

    Two dice, one question: probability = ways it can happen ÷ ways anything can happen.

    2min1:58

  3. Distributions

    the shape of chance

    Every outcome gets a probability; the whole picture is a distribution, and its shape tells you what to expect.

    2min1:53

  4. Expected value

    the long-run average

    Each outcome times its probability, added up: what average luck pays, and how casinos price everything.

    2min1:43

  5. Spread

    when averages lie

    Same average, different risk. Variance and standard deviation measure the honesty an average leaves out.

    2min2:08

  6. Conditional probability

    given that…

    Information shrinks the universe before you count. Every 'given' redraws the odds.

    2min2:12

  7. Bayes

    updating your beliefs

    Belief before, evidence, belief after — the spam-filter arithmetic of changing your mind.

    2min2:23

  8. The law of large numbers

    why the house wins

    Short runs are noisy, long runs are honest. Randomness rules the next flip; arithmetic rules the next million.

    2min2:15

  9. The normal distribution

    the bell that rings everywhere

    Add up many small random things and one shape appears every time. The bell curve, on purpose.

    2min2:21

  10. Sampling

    the spoonful and the soup

    Measure a few, conclude about all — why a stirred spoonful beats drinking the pot, and what bias breaks.

    2min1:59