课程19 Variance 编程

Mean

#Complete the mean function to make it return the mean of a list of numbers

data1=[49., 66, 24, 98, 37, 64, 98, 27, 56, 93, 68, 78, 22, 25, 11]

def mean(data):
    #Insert your code here
    return sum(data)/len(data)

Mode

#Complete the mode function to make it return the mode of a list of numbers
data1=[1,2,5,10,-20,5,5]
def mode(data):
    #Insert your code here
    modecnt=0
    for i in range(len(data)):
        icount=data.count(data[i])
        if icount>modecnt:
        mode=data[i]
        modecnt=icount
    return mode
print mode(data1)

Variance

#Complete the variance function to make it return the variance of a list of numbers
data3=[13.04, 1.32, 22.65, 17.44, 29.54, 23.22, 17.65, 10.12, 26.73, 16.43]
def mean(data):
    return sum(data)/len(data)
def variance(data):
    #Insert your code here
    mu=mean(data)
    return mean([(x-mu)**2 for x in data])

方差计算-我的算法

老师算法

课程20 Problem set 3 Estimators

练习1 MLE proof （optional ) -- 不理解

Standard score

用公式表示为：z=(x-μ)/σ;其中z为标准分数；x为某一具体分数，μ为平均数，σ为标准差

练习3 Scale Data
数据n倍，均值n倍，标准差n倍, 方差n方倍，z 分数不变。

练习7 Expected Variance

Variance - correction factor n/(n-1)

练习12 Likelihood challenge

#Compute the likelihood of observing a sequence of die rolls
#Likelihood is the probability of getting the specific set of rolls 
#in the given order
#Given a multi-sided die whose labels and probabilities are 
#given by a Python dictionary called dist and a sequence (list, tuple, string) 
#of rolls called data, complete the function likelihood
#Note that an element of a dictionary can be retrieved by dist[key] where
#key is one of the dictionary's keys (e.g. 'A', 'Good'). 

def likelihood(dist,data):
    #Insert your answer here
    p=1
    for d in data:
        p*=p*dist[d]
    return p

课程21 Outliers 异常值

有意忽略数据
Quartile interquartille
Percentile
忽略数据，计算均值，四分位，Trimmed mean(切尾平均数 截尾均值），百分位

课程22 Binomial Distribution 二项分布

组合计算 阶乘 概率

组合概率

课程23 Central Limit Theorem

杨辉三角

课程24 编程 Bell Curve

#Write a function flip that simulates flipping n fair coins. 
#It should return a list representing the result of each flip as a 1 or 0
#To generate randomness, you can use the function random.random() to get
#a number between 0 or 1. Checking if it's less than 0.5 can help your 
#transform it to be 0 or 1

import random
from math import sqrt

def mean(data):
    return float(sum(data))/len(data)

def variance(data):
    mu=mean(data)
    return sum([(x-mu)**2 for x in data])/len(data)

def stddev(data):
    return sqrt(variance(data))
    

def flip(N):
    #Insert your code here
    return [random.random()>0.5 for i in range(N)]

N=1000
f=flip(N)

print mean(f)
print stddev(f)

#Write a function sample that simulates N sets of coin flips and
#returns a list of the proportion of heads in each set of N flips
#It may help to use the flip and mean functions that you wrote before

import random
from math import sqrt
from plotting import *

def mean(data):
    return float(sum(data))/len(data)

def variance(data):
    mu=mean(data)
    return sum([(x-mu)**2 for x in data])/len(data)

def stddev(data):
    return sqrt(variance(data))
    

def flip(N):
    return [random.random()>0.5 for x in range(N)]
    
def sample(N):
    #Insert your code here
    return [mean(flip(N)) for x in range(N)]

N=1000
outcomes=sample(N)
histplot(outcomes,nbins=30)

print mean(outcomes)
print stddev(outcomes)