分保
The Drunkard’s Walk How Randomness Rules Our Lives The Drunkard’s Walk: How Randomness Rules Our Lives
Leonard Mlodinow (Pantheon, 2008)
We habitually underestimate the effects of randomness
a. Random events often come in groups/streaks/clusters
b. Extraordinary events can happen without extraordinary caus.
a. Hollywood movies
b. Home-run streaks
Laws of Probability
a. The probability that two events will both occur can never be greater than the probability that each will occur individually.
a. Assume Linda is a person drawn at random from the NY City phone book.
What is the relative probability ranking of the statements:
i. Linda is active in the feminist movement
ii. Linda is a psychiatric social worker
iii. Linda is a bank teller and is active in the feminist movement iv. Linda is a teacher in an elementary school
v. Linda is a member of the League of Women Voters
vi. Linda is a bank teller
vii. Linda is an insurance salesperson
b. Availability bias—in reconstructing the past, we give unwarranted
importance to memories that are most vivid (and hence most available for
retrieval)
41号随想
i. Which is greater?
1. # of 6-letter English words having an n as the fifth letter
2. # of 6-letter English words ending in ing ?
c. “A good story is of ten less probable than a less satisfactory [explanation]”
(Kahneman & Tversky)
b. If two possible events, A and B, are independent, then the probability that both A & B will occur is equal to the product of their individual probabilities.
c. If an event can have a number of different and distinct possible outcomes (A, B, C, and so on) then the probability that either A or B will occur is equal to the sum of the individual probabilities of A and B (and the sum of the probabilities of all the possible outcomes is 1.0, or 100%).
a. What are the odds that a couple are guilty of a crime in Los Angeles, given
that eyewitness described the culprits as “a Caucasian woman with a
blond ponytail…and a Black man with a beard and moustache who was driving a partl y yellow automobile” when the odds are:
i. 1/10 Partly yellow automobile
ii. ? Man with a moustache
iii. 1/10 Black man with a beard
iv. 1/10 Girl with ponytail
v. 1/3 Girl with blond hair
vi. 1/1,000 interracial couple in car
The Monty Hall Problem: 3 doors, a Marati behind 1 of them. After your first choice,
one door is opened, and you may change your choice or stay. Which is the better option? a. Law of “sample space”: Suppo a random process has many equally likely
outcomes, some favorable (winning), some unfavorable (losing). The probability
of obtaining a favorable outcome is equal to the proportion of outcomes that are
favorable.
The Law of Large Numbers (“Bernoulli?s Theorem”)
a. As we increa the number of trials, obrved frequencies will reflect—more and
more accurately—their underlying probabilities.
a. Law of Small Numbers: mistaken intuition that a small sample accurately
123什么意思reflects underlying probabilities.
b. General application: “One should not apprai (individual) human action
on the basis of its results”—implications for “outcomes bad”
management?
c. Specific ca: “Gambler?s fallacy”—mistaken notion that an event is
more or less likely to occur becau it has not happened recently Conditional Probability—Bayes? Theorem
a. We obrve a small sample of outcomes, from which we infer information and
make judgments about the qualities that produced tho outcomes. How should
we make tho inferences?
a. What is the probability that a family with two children has two daughters?
What is the probability that a family with two children has two daughters
if one is named Mary?
b. The conditional (“if”) “prunes” the sample space.
b. Bayes? theory shows that the probability that A will occur if B occurs will
generally differ from the probability that B will occur if A occurs.
a. What is the probability that an athlete is guilty of doping,
given that the
fal positive rate on the urine test is 1% and that the fal negative rate is
50%, and that the true rate of doping is 10%?
b. Procutor?s fallacy—inversion of conditionals.
i. 1/2500 battered women are murdered—but this is the wrong
statistic. 90% of battered women who are murdered, were儿科疾病
murdered by their spou.
中国现任大将c. Probability concerns predictions bad on fixed probabilities. Statistics infer
tho probabilities bad on obrved data.
Measurement Theory
a. Two issues:红参作用
a. How to determine a number that can summarize a measure of quality,
from a ries of varying measurements?
i. Nature of variation in data caud by random error (standard
deviation)
b. Given a limited t of measurements, how to asss the
probability that the
determination is correct?
i. Central limit theorem—deviations will be disperd in a normal
小虾distribution
b. Regression to th e mean: “A statistical enmble of people acting randomly often displays behavior as consistent and predictable as a
group of people pursuing conscious goals”—200,000 randomly acting
好玩的故事drivers can create a creature of habit
a. Much of the order we perceive in nature belies an invisible underlying
