概率学 英文(概率论 英文表达)

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n种可能结果：has n possible outcomes

总共有r种可能性：overall there are r possibilities for the whole experiment

关于。。。的假设：assumptions about。。

在。。的假设下：under various assumptions

如何收集样本：how the samples are collected

n中采样k个：gives the number of possible samples of size k out of a population of size n

有序，无序：order matters，not matter

有放回，无放回：with replacement，without replacement

如果所有的结果是等可能的，则事件A发生的概率为：If all outcomes are equally likely, the probability of an event A happening is.

A是否发生与B是否发生无关：whether A occurred gives no information about whether B occurred

独立事件：independent events

条件独立：conditional independence

A与B独立当且仅当下面等价命题成立：A and B are independent if and only if one of the following equivalent statements holds.

A与B在C下是条件独立的：A and B are conditionally independent given C

条件独立并不意味着独立：conditional independence does not imply independence

并，交，补：union，intersection，complements

德摩根定律：De Morgan's Laws，将并（交）的计算转化为交（并）的等式：A identity that can make caculating probabilities of unions easier by relating them to intersections, and vice versa.

辛普森悖论：Simpson's Paradox

全概率定理：Law of Total Probability

贝叶斯法则：Bayes' Rule

联合概率，边际概率，条件概率：joint probability, marginal probability, conditional probability

所有适用于概率的定理也适用于条件概率：Any theorem that holds for probability also holds for conditional probability

样本空间的一个分割：a partition of the sample space

他们是不相交的：they are disjoint

他们的并是整个样本空间：their union is the entir sample space

特例：special case

我们还可以写成：we can also write

A的后验是似然比乘先验：The posterior odds of A are the likelihood ratio times the prior odds.

概率质量函数：probability mass function

概率密度函数：probability density function

累积分布函数：cumulative distribution function

给定一个离散变量在取得某一值的概率：gives the probability that a discrete random variable takes on the value x.

a 满足：a satisfies

一个随机变量小于等于x：a random variable is less than or equal to x.

CDF是递增的，右连续的函数，且：CDF is an increasing, right-continuous function with...

一个与另一个无关：one gives no information about the other.

期望：expected value，mean，expectation，average

加权平均：weighted average

正式的，公式化的，数学上的,更一般地：more formally，mathematically, more generally

常数：constants

相同的分布意味着相同的均值：same distribution means same mean

在事件A下：conditioned on event A

如果事件发生，指示为1，否则为0：if the event occurs, the indicator is 1; otherwise it is 0.

在一个区间：in an interval

差：difference

。。。的导数：the derivative of ...

非负且和为1：A PDF is nonnegative and integrates to 1.

依据微积分的基本定理：by the fundamental theorem of calculus

随机变量在一定区间内的值：CRV takes on a value in an interval

将这一区间上的PDF累积：integrate the PDF over that interval

累加x乘PMF（离散）：sum x times the PMF

累加x乘PDF（连续）：integrate x times the PDF

X的期望定义如下：the expected value of X is defined this way:

也是：is also

万流归宗：universality of Uniform （plug a CRV into its own CDF, get a Uniform(0, 1)）

无意识统计学家定律：The Law of Unconscious Statistician

将x替换成X：plug X into x

让X的均值为mu，标准差为sigma：Let X have mean mu and standard deviation sigma.

均值，方差，偏差，峰值：mean，variance，skewness，kurtosis

泰勒展开式：Taylor expansion

他们分布相同：They are distributed the same

之和，之积：the sum of 。。 the product of。。

在离散/连续情况：in the discrete/continuous case

联合分布，条件分布，边际分布：joint distribution, conditional..., maginal ...

当且仅当下列条件满足：if and only if any of the following conditions holds

表示：denote

与。。相似：be analogous to ..

。。的近似：the analog of ...

属于-1,1：between-1 and 1

相反情况不一定对：the converse is not necessarily right

X,Y是独立同分布的：X, Y are identically distributed

对于任意常数a，b且a，b补位零：for any constants a, b with a and b nonzero

位置不变的，尺度不变的：location-invariant, scale-invariant

函数g是可微分的，严格递增的：the function g is differentiable and strictly increasing(decreasing)

雅克比，雅克比矩阵：Jacobian, Jacobian matrix

矩阵的行列式：the determinant of the matrix/ matrix's determinant

卷积积分：convolution integral

两个独立随机变量X，Y之和：the sum of two independent CRVs X and Y

独立同分布：i.i.d.

泊松过程：Poisson Process

每单位时间x到达：x arrivals per unit time

在长度为t的时间间隔内：in a time interval of length t

不相交的时间间隔：disjoint time interval

二元性，对偶性：duality

顺序统计量：order statistics

将他们从最小到最大排列：arrange them from smallest to largest

10次独立伯努利实验：10 independent Bernoulli trials

假设：given that

无记忆性属性：memoryless property

在前三次实验中：among the first 3 trails

亚当定律：Adam's Law a.k.a. Law of Total Expectation

Eve's Law: a.k.a. Law of Total Variance

大数定律：Law of Large Numbers

中心极限定理：Central Limit Theorem

样本均值：sample mean

收敛至：converge to。。

近似分布的：approximately distributed

换句话说：in other words

X is distributed 。。

连续分布：continuous distribution

均匀分布：Uniform Distribution

指数分布: Exponential Distribution

gamma分布：Gamma Distribution

β分布：Beta distribution

二项分布的共轭先验：conjugate prior of Binomial

卡方分布：Chi-Square distribution

离散分布：discrete distribution

二项分布：Binomial

伯努利分布：Bernoulli..

几何分布：Geometric..

一次成功分布：First Success..

负二项分布：Negative Binomial ..

超几何分布：Hypergemetric ..

泊松分布：Poisson ..

多元分布：multivariant..

多项式分布：Multinomial

多元高斯分布：multivariant normal ...

多元均匀分布：multivariant uniform...

公式：formulas

几何级数、等比级数：geometric series

积分：integrals

调和：Harmonic

欧拉逼近：Euler's approximation

阶乘的Stirling逼近：Stirling's approximation