Micro Learning - Math Shorts

#counting #rung1

Counting outcomes

@count.it

#EV #probability

The average roll of a fair die

@expected.value

#marginals #rung2

Marginals

@sum.the.row

#geometric #waitingtime

Rolls of a die until the first six

@wait.for.it

#totalprobability #rung3

Total probability

@split.the.cases

#gauss #sums

1 + 2 + 3 + ... + n

@sum.it

#expectation #rung4

First-step expectation

@how.long.until

#hypergeometric #rung5

Hypergeometric

@without.replacing

#geometric #coins

Flips until the first head

@fair.coin

#counting #rung1

Counting outcomes

@count.it

#marginals #rung2

Marginals

@sum.the.row

#markov #coins

Flips until two heads in a row

@two.in.a.row

#totalprobability #rung3

Total probability

@split.the.cases

#expectation #rung4

First-step expectation

@how.long.until

#markov #coins

Flips until a head then a tail

@head.then.tail

#hypergeometric #rung5

Hypergeometric

@without.replacing

#counting #rung1

Counting outcomes

@count.it

#montyhall #conditioning

Monty Hall: should you switch?

@switch.always

#marginals #rung2

Marginals

@sum.the.row

#totalprobability #rung3

Total probability

@split.the.cases

#birthdayparadox #pairs

23 people, a shared birthday?

@shared.days

#expectation #rung4

First-step expectation

@how.long.until

#couponcollector #EV

Rolls until you have seen every face

@collect.them.all

#symmetry #cards

Cards turned until the first ace

@cut.the.deck

#orderstatistics #dice

Expected value of the larger of two dice

@take.the.bigger

#dice #counting

The most likely sum of two dice

@roll.two

#optimalstopping #EV

Roll a die, reroll once if you want. Value?

@one.mulligan

#gamblersruin #martingale

Fair bets from k dollars: reach N before 0?

@fair.game

#paradox #EV

The St. Petersburg game: fair price?

@name.your.price

#geometry #probability

Break a stick at two random points. Triangle?

@snap.snap

#counting #classic

Three ants on a triangle walk off. No collision?

@no.collision

#conditioning #bayes

A card's top is black. Other side black too?

@other.side

from Bertrand's box

#bayes #basrate

1% sick, test 80% true, 5% false. Positive - sick?

@base.rate

from Pitman, Probability §1.5

#independence #proof

Independence survives complements

@independence

from Pitman, Ch 1 Review #6

#cards #conditioning

Deal until the first heart

@deal.until

from Pitman, Ch 1 Review #8

#totalprobability #bayes

Total probability, inside an event

@condition.inside

from Pitman, Ch 1 Review #13

#binomial

8 shots, each hits with p = 0.7

@n.choose.k

from Pitman, Exercise 2.1.6

#binomial #pascal

P(k−1 heads | k−1 or k heads)

@pascal.trick

from Pitman, Exercise 2.1.10

#independence #binomial

Two independent traits, ten offspring

@two.traits

from Pitman, Exercise 2.1.14

#hypergeometric #support

How many good can a sample hold?

@what.is.possible

from Pitman, Exercise 2.5.11

#counting #poker

Poker hands, counted from scratch

@count.the.hand

from Pitman, Exercise 2.5.12

#totalprobability

Two urns, pick one at random, draw a ball. Black?

@pick.an.urn

from Pitman, Probability §1.4