meta统计系统整理 +题目

1)  Bernoulli Trial : 2 possible outcome Success = 1  failure  = 0
x is success P(X = x) = p^x (1-p)^1-x  ， Mean( expected value) = E[X] = P ， Variance: Var(X) = p(1-p)  ，Standard Deviation = 根号 p(1-p)  
2）binomoal distribution ： Mean(expected value) = E[X] = np Variance : Var(X) = np(1-p) Standerdevaitaion = 根号 np(1-p)
3）Bionomal coefficient: { n k} means number of ways choose k success from n trials
4）complementary Probability： 1 - P1)     Law of total Probability
5） Law of total Probability： P(X) = B1 * P(X) + B2 *(PX) + B3 * P(X) = total probaibility randomly
6）Conditional Probability ： P(A|B) = P( A and B) / P(B) 
7）Bayes’ rule : P(A|B) = P(B|A)P(A)/ P(B)
8） Central limit  / large number
基础的掌握这些概念 应用到题目中基本就是涉及这些了 下面是一些具体的考试题目， 希望加加米！
Impression 
X people, 一共有Y Impression随机分配 
1) expected impression per audience？ 
For one impression, the prob one person will see = 1/X (Each ad has uniform 1/X prob to be seen). n次实验成功了m次的binomial distribution 
p=1/X, n=Y 
E = np = Y/X 
Let's check all the requirements of binomial distribution are valid: 
1. Trials are independent (because we can assign an impression to any people irrespective of whether they already saw an impression or not) 
2. Fixed number of trials (Y) 
3. P(success) is the same across trials (1/X for every impression assignment we have to do) 
2) probability of each person have at least one impression 
For one user 
- the prob of seeing no impression = (1-1/X)^Y 
- the prob that he/she will see at least 1 ad = 1-(1-1/X)^Y 
~= 1-(1-Y/X) = Y/X 
这里用到了tyler expansion on binomial coefficient: (1 + x)^a ~= 1 + ax 需要X很大 
3) expected number of audience have at least one impression 
the number of people who will see at least one impression = X * (1-(1-Y/X)

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Curated Interview Questions from Top Companies

问trends for day 2-30 
如果是一个trend：a fluctuating curve with larger value during weekends and smaller value during weekdays. If we are running any campaigns or suppose FB is healthily growing and increasing user engagement, there might be an increase in the values in general. 如果是其中某一天的dist：波动比较大的长尾分布 
如果是average daily dist：比较稳定的长尾分布 
d. 取出day 1 所有page share=5的population, 问同样的trend。和c比哪个方差大 ，是什么分布？ 
a similar fluctuating curve with larger average # of sharing and smaller variance/smaller gap between weekends and weekdays. c has larger variance because users are not as engaged as users with 5 shares per day - they can just share two posts by chance. 
2. dist of time spent per user，一般是一个right skewed dist
a. 画出5%，median，mean,95%，以及他们分别在未来三周的dist 
* average time spent on FB is around 35min per day 
p5: 0min 
median: 30min 
mean: 35min 
p95: 100min 
未来三周的dist: a fluctuating curve with larger value during weekends and smaller value during weekdays. Fluctuation is largering in p5, smaller in p95. 
b. 取出今天分布在mean的用户，他们在未来30天的time spent dist应该是怎样 的？Will the mean still be same or larger or smaller? 
A fluctuating curve with larger value during weekends and smaller value during weekdays. The mean will remain the same. 
Distribution of time spent/DAU 
假设所有人同时在线，每人下线几率独立于已在线时间，则服从exponential 
Distribution of #comments/DAU 
假设每人每看到一个post有独立的p的几率comment，p较小，impression较多，则服从 poisson 
帖子的总回复数、转发数之类的分布，不是确定时间内的 
社交网络的这些metric通常都是exponential 因为绝大部分帖子都没人回复 没人转发 一些名人 的回复转发非常多 长尾巴 左边0的特别多 

感谢楼主发帖，我正好在准备面试。
normal approximation: P(x>8) = P(z > (8-4)/3.84) = 1-pnorm(1.04) 这里应该是除以3.84开根号，不是3.84

感谢楼主整理的题目，可是没有提行和indent看得我怀疑人生😂