Probability

Dimitri di米tri
Pantelis 潘泰利斯
Bertsekas   b t sai ks

John
Nikos 尼ko斯
Tsitsiklis  c c k le s


Massachusetts
Athena  θ
mechanical  机械的
retrieval   恢复
bibliographical 书目性的
stochastic  随机

probability is common sense reduced to calculation
概率是常识，简化为计算
    -- Laplace


outgrowth
spectrum    光谱
exposition  ˌek-spə-ˈzi-shən    博览会
probabilistic    ˌprä-bə-bə-ˈli-stik
intuitive   直觉的
precision   精确
rigorous    严格的
theoretical ai
subtle      微妙的
hint        暗示
attentive   注意
discrete
theorem     定理
least squares estimation    最小二乘估计
bivariate   bai 二元正态分布
Bernoulli
Poisson  pwä-ˈsōⁿ- 
Markov Processes(马尔科夫过程)
stochastic
omission

Bayesian    bā-zē-ən 
bayes       zi
parameter estimation    参数估计
hypothesis
supplement  补充
theoretical  ruai 理论的
constitute   ˈkän(t)-stə-ˌtüt

recitation  ai  背诵
calibrate   校准
supplementary   补充
stand the test of time  经得起时间的考验
we are indebted to  ɪnˈdetɪd 我们欠
with the student body   与学生团体
robust

facilitate  促进
methodology 方法

correlation  r`e    相关性


chebyshev   切比雪夫
convergence 收敛
absorption  吸收
posterior   后部
is admitted to the hospital 住进了医院
administered

a concerned relative    关心此事的亲戚
relieved    松了口气
exasperated ig-ˈza-spə-ˌrā-təd  激怒了
what a sick thought
moderately  适度地
such an interpretation is often natural 这种解释往往是很自然的
roughly 大致
Iliad and the odyssey   《伊里亚特》和《奥德赛》
assertion
prerequisite    前提条件
dwell   唠叨
empirical    im-ˈpir-i-kəl  经验
reasoning   推理

at the outset   一开始
donoted by  表示为
finite
a coin toss is 扔
stands for

infinitely   ˈin-fə-nət-lē 
countably infinite

"|" such that

expedient   方便的，权宜     ik-ˈspē-dē-ənt
conceivably 可以想象地
disjoint    不相交的
partition   分割

Venn diagrams
algebra 代数
分配率

De Morgan's laws
长线变短线，符号要改变
converse inclusion  逆包含

accordance  按照
likelihood

event:  subset of sample space
finite nai
infinite
dart    镖
roll of a die
collectively exhaustive 穷尽
intricate   错综复杂
pathological    病态的
inherently  本质上
additivity  an
axiom   公理
counterpart 对方
sufficiently    充分地
subinterval 子区间
treatment   治疗
incidentally    `ci 顺便
legitimacy
hinge on the fact   以事实为准
contradict  顶撞
deduce  推断

P(AUBUC) = P(A) + P(A^nB) + P(A^nB^nC)
P(AUB)  = P(A)      + P(A^nB)
P(B)    = P(AnB)    + P(A^nB)

tractable   容易驾驭的
tradeoff    权衡
tractability    易处理性
inequality  i-ni
entail  蕴涵
no room for ambiguity   没有含糊的余地
conveivable 可以想象的
paradox 悖论
inconsistency
bertrand's paradox  贝特朗悖论
equilateral  ˌē-kwə-ˈla-tə-rəl 
inscribed   铭刻
contradictory   矛盾的
vertex  顶点
tangent 切线

algebraic    ˌal-jə-ˈbrā-ik
hindus  印度教徒
millennium  千年
Renaissance
Girolamo Cardano
Fermat and pascal   费马和帕斯卡
empirical   经验
astronomical    天文
axiomatic   公理化的

conditional probability of A given B, denoted by P(A|B).
P(A|B) = numof(AnB) / numof(B)
P(A|B) = P(AnB) / P(B)
disjoint
P(AUC|B) <= P(A|B) + P(C|B)
P(AnB) = P(B)P(A|B)

pervasively 普遍地
conservative    保守的
innovative
cumbersome  麻烦
conjunction 连词

P(AnBnC) = P(A)P(B|A)P(C|AnB)
        = P(A) * `P(AnB)/P(A)` * `P(AnBnC)/P(AnB)`

P(B) = P(A1nB) + ... P(AxnB) (partition)
    = P(A1)P(B|A1) + ...

Bayes' Rule
换头公式



scenario    设想
decomposed  分解的
tournament  比赛
opponent    对手
celebrated  著名
malignant   恶性的
tumor   
exhaustive  详尽的
posterior   后部

binomial
combinatorics
permutation 排列


INDEPENDENCE
P(A|B) = P(A)

P(AnB) = P(A)P(B)   判断公式
意味着  P(A|B) = P(A)       B不影响A（P(B) > 0), so as A and B^

Conditional Independence    条件独立

        = P(B|C)P(A|BnC)
P(AnB|C) = P(A|C)P(B|C)
意味着 P(A|BnC) = P(A|C)

无条件独立和条件独立不相关


两两互相独立，三个独立

homogeneous

1.6 COUNTING

================================================
2.1
instrument reading

discrete: finite or countable infinite
reputedly   据说
cavalry 骑兵
Celsius
Fahrenheit  ˈfærənhaɪt
logarithmic
monetary
converges   集中
torque  扭矩
variance    方差
dispersion  分散
standard deviation
概率质量函数

Py(y) = Sum( px(x) ) 
    in {x|g(x)=y}

weighted    有利于

E[X] = Sum(x p(x))
torque  扭矩

var(X) = E[ (X - E[X])^2 ]

dispersion  分散

standard deviation

Y = aX + b
E[Y] = aE[x] + b
var[Y] = a^2var[X]

var(X) = E[X^2] - (E[X])^2

uniformly distributed
E[x] = (a+b)/2;
var[x] = [b-a][b-a+2]/12

E[x^2] = (n+1)(2n+1)/6

babular method

linear:
    E[aX + bY + c] = aE[X] + bE[Y] + c

analogously
linearity


P(A) = sumof(P[{X=x} n A])

pertain
scrutinize  仔细检查