關係式表達 (1)：單一變數

# 布林值比較
TRUE==FALSE

## [1] FALSE

# 數值比較 (不等於)
-6 * 4 != 16-101

## [1] TRUE

# 比較字串
"useR"=="user"

## [1] FALSE

# 布林值與數值
TRUE==1

## [1] TRUE

FALSE==0

## [1] TRUE

關係式表達 (2) : 向量與矩陣

# 建立兩個向量 linkedin and facebook，表示兩種社交媒體中之人氣
linkedin <- c(16, 9, 13, 5, 2, 17, 14)
facebook <- c(17, 7, 5, 16, 8, 13, 14)

# 查看linkedin的人氣有沒有超過15
linkedin > 15

## [1]  TRUE FALSE FALSE FALSE FALSE  TRUE FALSE

# 查看linkedin的人氣有沒有低於5
linkedin <= 5

## [1] FALSE FALSE FALSE  TRUE  TRUE FALSE FALSE

# Linkedin是否比Facebook更有人氣
linkedin > facebook

## [1] FALSE  TRUE  TRUE FALSE FALSE  TRUE FALSE

# 合併為一個矩陣
views <- matrix(c(linkedin, facebook), nrow = 2, byrow = TRUE)

# 檢查矩陣的內容
views <= 14

##       [,1] [,2] [,3]  [,4] [,5]  [,6] [,7]
## [1,] FALSE TRUE TRUE  TRUE TRUE FALSE TRUE
## [2,] FALSE TRUE TRUE FALSE TRUE  TRUE TRUE

關係式表達 (3) : and (&) 和 or (|)

TRUE & TRUE

## [1] TRUE

FALSE | TRUE

## [1] TRUE

5 <= 5 & 2 < 3

## [1] TRUE

3 < 4 | 7 < 6

## [1] TRUE

關係式表達 (4) : and (&) 和 or (|)

# linkedin exceeds 10 but facebook below 10
linkedin >10 & facebook <10

## [1] FALSE FALSE  TRUE FALSE FALSE FALSE FALSE

# When were one or both visited at least 12 times?
linkedin>=12 | facebook >=12

## [1]  TRUE FALSE  TRUE  TRUE FALSE  TRUE  TRUE

# When is views between 11 (exclusive) and 14 (inclusive)?
views >11 & views<=14

##       [,1]  [,2]  [,3]  [,4]  [,5]  [,6] [,7]
## [1,] FALSE FALSE  TRUE FALSE FALSE FALSE TRUE
## [2,] FALSE FALSE FALSE FALSE FALSE  TRUE TRUE

If Structures

If…Else Structures 是撰寫程式必備的技巧之一，可以控制在不同的情況下讓電腦執行不同的程式

if (condition) {
  expr
}

範例：

x <- 10
if(x > 8)  # 如果 x > 8 則執行 {} 內的程式
{
 print("x is larger than 8")
}

## [1] "x is larger than 8"

If…Else Structures

if…else架構如下：

if (condition1) {
  expr1
} else if (condition2) {
  expr2
} else if (condition3) {
  expr3
} else {
  expr4
}

範例：

x <- 10
if(x > 8) { 
# 如果 x > 8，執行以下程式
 print("x is larger than 8")
} else if(x > 6) { 
# 如果 x > 6 且 x <= 8，執行以下程式
   print("x is larger than 6, but not larger than 8")
} else { 
# 其它所有情況下執行以下程式
  print("x is not larger than 6")
}

## [1] "x is larger than 8"

範例：

number <- 4
if (number < 10) {
  if (number < 5) {
    result <- "extra small"
  } else {
    result <- "small"
  }
} else if (number < 100) {
  result <- "medium"
} else {
  result <- "large"
}
#print(result)

while loop (1)

The while loop can be used to repeat a set of instructions, and it is often used when you do not know in advance how often the instructions will be executed.

while (condition) {
  expr
}

範例：

# 設定 speed的教值
speed <- 100

# Code the while loop
while (speed>30) {
  print("慢一點!")
  speed <- speed-18
}

## [1] "慢一點!"
## [1] "慢一點!"
## [1] "慢一點!"
## [1] "慢一點!"

print(speed)

## [1] 28

while loop (2): 结合if structure

# 設定 speed的教值
speed <- 100

while (speed > 30) {
  print(paste("現在速度是",speed))
  if (speed>48) {
    print("剎車踩大力一點!")
    speed <- speed -15
  } else {
    print("小力踩剎車!")
    speed <- speed -6
  }
}

## [1] "現在速度是 100"
## [1] "剎車踩大力一點!"
## [1] "現在速度是 85"
## [1] "剎車踩大力一點!"
## [1] "現在速度是 70"
## [1] "剎車踩大力一點!"
## [1] "現在速度是 55"
## [1] "剎車踩大力一點!"
## [1] "現在速度是 40"
## [1] "小力踩剎車!"
## [1] "現在速度是 34"
## [1] "小力踩剎車!"

while loop (3): break

The break statement is a control statement. When R encounters it, the while loop is abandoned completely.

範例：

# 設定 speed的教值
speed <- 120

while (speed > 30) {
  print(paste("你的速度是", speed))
  # 當速度超過100時離開loop
  if (speed>100) {
    print("剎不住了!!")
    break
  }
  if (speed>48) {
    print("剎車踩大力一點!")
    speed <- speed -15
  } else {
    print("小力踩剎車!")
    speed <- speed -6
  }
}

## [1] "你的速度是 120"
## [1] "剎不住了!!"

範例：猜猜看結果是什麼?

i <- 1
while (i <= 30) {
  print(i)
  if (i%%5==0) {
    break
  }
  i <- i*2 + 1
}

for Loops (1)

The for loop can be used to repeat a set of instructions, and it is used when you know in advance the values that the loop variable will have each time it goes through the loop.

範例：讀取vector

# 向量 linkedin 
linkedin <- c(16, 29, 16, 5, 2)

# Loop version 1
for (i in linkedin){
    print(i)
}

## [1] 16
## [1] 29
## [1] 16
## [1] 5
## [1] 2

# Loop version 2
for (i in 1:length(linkedin)){
    print(linkedin[i])
}

## [1] 16
## [1] 29
## [1] 16
## [1] 5
## [1] 2

範例：讀取list

primes_list <- list(2, 3, 5, 7, 11, 13)

# loop version 1
for (p in primes_list) {
  print(p)
}

## [1] 2
## [1] 3
## [1] 5
## [1] 7
## [1] 11
## [1] 13

# loop version 2
for (i in 1:length(primes_list)) {
  print(primes_list[[i]])
}

## [1] 2
## [1] 3
## [1] 5
## [1] 7
## [1] 11
## [1] 13

for Loops (2): 兩層for loop

x1 <- matrix(c("A","B","C","D","E","F"),nrow=2,byrow = TRUE)
x1

##      [,1] [,2] [,3]
## [1,] "A"  "B"  "C" 
## [2,] "D"  "E"  "F"

for (i in 1:nrow(x1)){
  for (j in 1:ncol(x1)){
    print(paste("第 ",i," 列和第 ",j," 行是 ",x1[i,j],sep=""))
  }
}

## [1] "第 1 列和第 1 行是 A"
## [1] "第 1 列和第 2 行是 B"
## [1] "第 1 列和第 3 行是 C"
## [1] "第 2 列和第 1 行是 D"
## [1] "第 2 列和第 2 行是 E"
## [1] "第 2 列和第 3 行是 F"

for Loops (3): break

# The linkedin vector has already been defined for you
linkedin <- c(16, 9, 13, 5, 2, 17, 14)

# Extend the for loop
for (li in linkedin) {
  if (li > 10) {
    print("You're popular!")
  } else {
    print("Be more visible!")
  }
  
  # Add if statement with break
  if (li>16) {
      print("This is ridiculous, I'm outta here!")
      break
  }
  
  # Add if statement with next
  if (li<5){
      print("This is too embarrassing!")
      next
  }
  
  print(li)
}

## [1] "You're popular!"
## [1] 16
## [1] "Be more visible!"
## [1] 9
## [1] "You're popular!"
## [1] 13
## [1] "Be more visible!"
## [1] 5
## [1] "Be more visible!"
## [1] "This is too embarrassing!"
## [1] "You're popular!"
## [1] "This is ridiculous, I'm outta here!"

for Loops (4): 字串處理

# Pre-defined variables
rquote <- "r's internals are irrefutably intriguing"
chars <- strsplit(rquote, split = "")[[1]]

# Initialize rcount
rcount <- 0

# Finish the for loop
for (char in chars) {
  if (char=="r"){
      rcount <- rcount+1
  }
  if(char=="u"){
      break
  }
}

# Print out rcount
print(rcount)

## [1] 5

計算從 1+2+3+…+100 的值

 x=0
 for (i in 1:100)
 {
 x <- x+i
 }
 show(x)

## [1] 5050

Question

請計算出1+3+5+…+101的值

Answer

 x <- 0
 for (i in seq(1,101,by=2))
 {
 x <- x+i
 }
 show(x)

## [1] 2601

 x <- 0
 for (i in seq(1,101,by=2))
 {
  if (i%%2==1) {x <- x+i}
 }
 show(x)

## [1] 2601

Questions: Central limit theorem (C.L.T)

Let the population distribution is {1,1,1,5,5,8,9,13,15,15,15,15}
Generate n sample from this population
Could you plot the sampling distribution of “sample mean” with different sample size?

Answers: Code

data <- c(1,1,1,5,5,8,9,13,15,15,15,15)
result <- mean(sample(data, n, replace=T))

for (i in 1:1000){
  x <- sample(data, n, replace=T)
  result <- c(result,mean(x))
}

hist(result, col = "gray")
#qqnorm(result)

Functions (1)

查詢函數功能

help(mean)
?mean

查詢函數參數

args(mean)

## function (x, ...) 
## NULL

args(sample)

## function (x, size, replace = FALSE, prob = NULL) 
## NULL

Functions (2): 使用函數

# 設定 linkedin 和 facebook
linkedin <- c(16, 9, 13, 5, 2, 17, 14)
facebook <- c(17, 7, 5, 16, 8, 13, 14)

# 計算其平均數
mean_li <- mean(linkedin)
mean_fb <- mean(facebook)

# 列印結果
print(mean_li)

## [1] 10.85714

print(mean_fb)

## [1] 11.42857

Functions (3): 使用函數

# 設定 linkedin 
linkedin <- c(16, NA, 13, 5, 2, 17, 14)
# 計算其平均數
mean(linkedin)

## [1] NA

#移除NA值
mean(linkedin,na.rm=TRUE)

## [1] 11.16667

Functions (4): Write your own function

若處理資料的過程中，有重覆或複雜性的工作，我們可以自己撰寫函數來幫助我們完成任務。函數 (function)的架構如下：

my_fun <- function(arg1, arg2) {
  body
}

範例：

# 創造一個函數，命名為 hello()
hello <- function(){
    print("您好!")
    return(TRUE)
}

# 測試一下
hello()

## [1] "您好!"

## [1] TRUE

# 創造一個函數，命名為 pow_two()
pow_two <- function(a){
    pow_two <- a^2
}
# 測試一下
pow_two(12)

# 創造一個函數，命名為 sum_abs()
sum_abs <- function(x,y){
    abs(x)+abs(y)
}
# 測試一下
sum_abs(-2, 3)

## [1] 5

(註) 函數中，回傳值的方式有很多種：

寫在最後一行
指定給函數變數
使用reutrn()

Functions (5): Write your own function

函數參數可以設定其 deafult value，其架構如下：

my_fun <- function(arg1, arg2 = val2) {
  body
}

範例

pow_two <- function(x, print_info=TRUE) {
  y <- x ^ 2
  if (print_info){
  print(paste(x, "to the power two equals", y))
  }
  return(y)
}
pow_two(10)

## [1] "10 to the power two equals 100"

## [1] 100

pow_two(10, FALSE)

## [1] 100

Probability Distributions (機率分配)

We look at some of the basic operations associated with probability distributions. There are a large number of probability distributions available, but we only look at a few.
If you would like to know what distributions are available you can do a search using the command help(Distributions).
For every distribution there are four commands. The commands for each distribution are prepended with a letter to indicate the functionality:
- “d” returns the height of the probability density function
- “p” returns the cumulative density function
- “q” returns the inverse cumulative density function (quantiles)
- “r” returns randomly generated numbers

probability density function

\[ p(x) <- \frac{1}{\sigma \sqrt{2 \pi}} e^{-\frac{(x-\mu)^2}{2 \sigma^2}} \]

dnorm(0)

## [1] 0.3989423

dnorm(0)*sqrt(2*pi)

## [1] 1

dnorm(0,mean=4,sd=10)

## [1] 0.03682701

v <- c(0,1,2)
dnorm(v)

## [1] 0.39894228 0.24197072 0.05399097

Plot N(0,1)

x <- seq(-20,20,by=.1)
y <- dnorm(x)
plot(x,y)

Plot N(1,3)

x <- seq(-20,20,by=.1)
y <- dnorm(x,mean=1,sd=3)
plot(x,y,type="l")

Cumulative density function (CDF)

pnorm(0)

## [1] 0.5

pnorm(1)

## [1] 0.8413447

pnorm(0,mean=2)

## [1] 0.02275013

pnorm(0,mean=2,sd=3)

## [1] 0.2524925

Plot CDF of Normal Distribution

x <- seq(-5,5,by=.05)
y <- pnorm(x)
plot(x,y,type="l")

Inverse CDF (quantiles)

qnorm(0.5)

## [1] 0

qnorm(0.5,mean=1)

## [1] 1

qnorm(0.5,mean=1,sd=2)

## [1] 1

qnorm(0.25,mean=2,sd=2)

## [1] 0.6510205

Randomly generated numbers (Normal)

rnorm(4)

## [1]  0.44268722  0.64946309 -0.04129442 -0.04362132

rnorm(4,mean=3,sd=3)

## [1]  2.949999  3.159914 -1.796055  2.050207

Randomly generated numbers (Normal)

y <- rnorm(500)
hist(y)

Question: Monte Carlo Simulation

蒙地卡羅方法又稱統計模擬法、隨機抽樣技術，是一種隨機模擬方法，以概率和統計理論方法為基礎的一種計算方法，是使用隨機產生資料來解決很多計算問題的方法。
假如我們不知道半徑為 1 的圓形面積，那麼就可以利用亂數隨機取樣 1百萬個 X=random[-1…1], Y=random[-1…1] 之間的的值，然後看看有多少點落在圓的範圍之內。最後利用 4 * [落在圓內點的比率] 就可以計算出該圓形的面積。
提示：runif()

Answer

# 圓面積的估計
n <- 5000
x <- runif(n, min = -1, max = 1)
y <- runif(n, min = -1, max = 1)
r <- x^2+y^2
length(r[r<1])/n*4

## [1] 3.1496

apply 函數家族 (1): lapply()

lapply returns a list of the same length as X, each element of which is the result of applying FUN to the corresponding element of X.

lapply(X, FUN, ...)
# ...   optional arguments to FUN.

範例：

x <- list(a = 1:10, beta = exp(-3:3), logic = c(TRUE,FALSE,FALSE,TRUE))
# compute the list mean for each list element
lapply(x, mean)

## $a
## [1] 5.5
## 
## $beta
## [1] 4.535125
## 
## $logic
## [1] 0.5

# median and quartiles for each list element
lapply(x, quantile, probs = 1:3/4)

## $a
##  25%  50%  75% 
## 3.25 5.50 7.75 
## 
## $beta
##       25%       50%       75% 
## 0.2516074 1.0000000 5.0536690 
## 
## $logic
## 25% 50% 75% 
## 0.0 0.5 1.0

apply 函數家族 (2): lapply()

# Write function select_second()
select_second <- function(x) {
  x[2]
}
x <- list(a = 1:10, beta = exp(-3:3), logic = c(TRUE,FALSE,FALSE,TRUE))
# 使用 select_second() 取得需要的資料
lapply(x, select_second)

## $a
## [1] 2
## 
## $beta
## [1] 0.1353353
## 
## $logic
## [1] FALSE

apply 函數家族 (3): lapply()

# Generic select function
select_el <- function(x, index) {
  x[index]
}
x <- list(a = 1:10, beta = exp(-3:3), logic = c(TRUE,FALSE,FALSE,TRUE))
# 使用 select_second() 取得需要的資料
lapply(x, select_el, index=2)

## $a
## [1] 2
## 
## $beta
## [1] 0.1353353
## 
## $logic
## [1] FALSE

apply 函數家族 (4): sapply()

You can use sapply() similar to how you used lapply().

sapply(X, FUN, ...)

範例：See how lapply() and sapply() differ

temp <- list(a = 1:10, beta = exp(-3:3), logic = c(TRUE,FALSE,FALSE,TRUE))

# Use lapply() to find each factor's minimum
lapply(temp, min)

## $a
## [1] 1
## 
## $beta
## [1] 0.04978707
## 
## $logic
## [1] 0

# Use sapply() to find each factor's minimum
sapply(temp,min)

##          a       beta      logic 
## 1.00000000 0.04978707 0.00000000

# Use lapply() to find each factor's maximum 
lapply(temp, max)

## $a
## [1] 10
## 
## $beta
## [1] 20.08554
## 
## $logic
## [1] 1

# Use sapply() to find each factor's maximum
sapply(temp, max)

##        a     beta    logic 
## 10.00000 20.08554  1.00000

apply 函數家族 (5)

extremes <- function(x) {
  c(min = min(x), max = max(x))
}

temp <- list(a = 1:10, beta = exp(-3:3), logic = c(TRUE,FALSE,FALSE,TRUE))
# Apply extremes() over temp with sapply()
sapply(temp, extremes)

##      a        beta logic
## min  1  0.04978707     0
## max 10 20.08553692     1

# Apply extremes() over temp with lapply()
lapply(temp, extremes)

## $a
## min max 
##   1  10 
## 
## $beta
##         min         max 
##  0.04978707 20.08553692 
## 
## $logic
## min max 
##   0   1

其它常用技巧(1): 數值函數

abs(): calculate the absolute value.
sum(): calculate the sum of all the values in a data structure.
mean(): calculate the arithmetic mean.
round(): Round the values to 0 decimal places by default.

範例：

errors <- c(1.9, -2.6, 4.0, -9.5, -3.4, 7.3)
sum(abs(round(errors)))

## [1] 29

其它常用技巧(2): 資料處理函數

seq(): Generate sequences, by specifying the from, to and by arguments.
rep(): Replicate elements of vectors and lists.
sort(): Sort a vector in ascending order. Works on numerics, but also on character strings and logicals.
rev(): Reverse the elements in a data structures for which reversal is defined.
str(): Display the structure of any R object.
append(): Merge vectors or lists.
is.*(): Check for the class of an R object.
as.*(): Convert an R object from one class to another.
unlist(): Flatten (possibly embedded) lists to produce a vector.

範例：

x <- seq(1,20,by=2)
y <- append(x,rep(c(4,6),2))
sort(y)

##  [1]  1  3  4  4  5  6  6  7  9 11 13 15 17 19

sort(y,decreasing = TRUE)

##  [1] 19 17 15 13 11  9  7  6  6  5  4  4  3  1

list_y<-as.list(y)
str(list_y)

## List of 14
##  $ : num 1
##  $ : num 3
##  $ : num 5
##  $ : num 7
##  $ : num 9
##  $ : num 11
##  $ : num 13
##  $ : num 15
##  $ : num 17
##  $ : num 19
##  $ : num 4
##  $ : num 6
##  $ : num 4
##  $ : num 6

vector_y <- unlist(y)
str(vector_y)

##  num [1:14] 1 3 5 7 9 11 13 15 17 19 ...

其它常用技巧(3): Regular Expressions

Regular Expression 稱為正則表達式，又稱為正規表達式或正規表示式。
由於Regular Expression是一種利用特用字元及一些資料的標定、搜尋及替換的規則。
在R中能以內建的函數完成相關工作，但是若要真正熟悉Regular Expression完整功能，則需要花上許多時間去練習、測試。
Sequence of characters
Pattern existence
Pattern replacement
Pattern extraction
grep(), grepl()
sub(), gsub()

其它常用技巧(4): Regular Expressions

範例

emails <- c("john.doe@ivyleague.edu", "education@world.gov", "dalai.lama@peace.org",
            "invalid.edu", "quant@bigdatacollege.edu", "cookie.monster@sesame.tv")
# Use grepl() to match for "edu"
grepl("edu",emails)

## [1]  TRUE  TRUE FALSE  TRUE  TRUE FALSE

# Use grep() to match for "edu", save result to hits
hits <- grep("edu",emails)
# Subset emails using hits
emails[hits]

## [1] "john.doe@ivyleague.edu"   "education@world.gov"     
## [3] "invalid.edu"              "quant@bigdatacollege.edu"

其它常用技巧(5): Regular Expressions

上一頁的範例中，有一個錯誤的結果，我們需要更進一步的設定 Regular Expressions

範例

emails <- c("john.doe@ivyleague.edu", "education@world.gov", "dalai.lama@peace.org",
            "invalid.edu", "quant@bigdatacollege.edu", "cookie.monster@sesame.tv")
# Use grepl() to match for .edu addresses more robustly
grepl("@.*\\.edu$",emails)

## [1]  TRUE FALSE FALSE FALSE  TRUE FALSE

# Use grep() to match for .edu addresses more robustly, save result to hits
hits <- grep("@.*\\.edu$",emails)

# Subset emails using hits
emails[hits]

## [1] "john.doe@ivyleague.edu"   "quant@bigdatacollege.edu"

說明：

@, because a valid email must contain an at-sign.
.*, which matches any character (.) zero or more times (*). Both the dot and the asterisk are metacharacters. You can use them to match any character between the at-sign and the “.edu” portion of an email address.
\\.edu$, to match the “.edu” part of the email at the end of the string. The \\ part escapes the dot: it tells R that you want to use the . as an actual character.

其它常用技巧(6): Regular Expressions

sub() and gsub(): you can specify a replacement argument. If inside the character vector x, the regular expression pattern is found, the matching element(s) will be replaced with replacement.
sub() only replaces the first match, whereas gsub() replaces all matches.

emails <- c("john.doe@ivyleague.edu", "education@world.gov", "dalai.lama@peace.org", 
            "invalid.edu", "quant@bigdatacollege.edu", "cookie.monster@sesame.tv")

# Use sub() to convert the email domains to test.edu
sub("@.*\\.edu$","@test.edu",emails)

## [1] "john.doe@test.edu"        "education@world.gov"     
## [3] "dalai.lama@peace.org"     "invalid.edu"             
## [5] "quant@test.edu"           "cookie.monster@sesame.tv"

Question

若取得以下電影review字串資料 (from IMDB)，我們想知道覺得該評論有用的比率是多少?

mydata <- c("3061 out of 4024 people found the following review useful",
            "1061 out of 2424 people found the following review useful",
            "61 out of 124 people found the following review useful",
            "9 out of 24 people found the following review useful")

Answer

mydata <- c("3061 out of 4024 people found the following review useful",
            "1061 out of 2424 people found the following review useful",
            "61 out of 124 people found the following review useful",
            "9 out of 24 people found the following review useful")
x1 <- as.numeric(sub(" out.*useful","",mydata))
y1 <- sub(" people found the following review useful","",mydata)
y1 <- as.numeric(sub(".*of ","",y1))
rating <- x1/y1
print(rating)

## [1] 0.7606859 0.4377063 0.4919355 0.3750000

其它常用技巧(7): 日期與時間

Date objects store the number of days since the 1st of January in 1970.

# Get the current date: today
today <- Sys.Date()

# See what today looks like under the hood
unclass(today)

## [1] 17079

# Get the current time: now
now <- Sys.time()

# See what now looks like under the hood
unclass(now)

## [1] 1475605132

其它常用技巧(8): 日期與時間

To create a Date object from a simple character string in R, you can use the as.Date() function.

%Y: 4-digit year (1982)
%y: 2-digit year (82)
%m: 2-digit month (01)
%d: 2-digit day of the month (13)
%A: weekday (Wednesday)
%a: abbreviated weekday (Wed)
%B: month (January)
%b: abbreviated month (Jan)

# Definition of character strings representing dates
str1 <- "2012-03-15"
str2 <- "30/5/2016"

# Convert the strings to dates: date1, date2
date1 <- as.Date(str1, format="%Y-%m-%d")
date2 <- as.Date(str2, format="%d/%m/%Y")

# Convert dates to formatted strings
format(date1, "%A")

## [1] "周四"

format(date2, "%d")

## [1] "30"

format(date2, "%b %Y")

## [1] " 5 2016"

其它常用技巧(9): 日期與時間

# a useful package for creating a Date object
library(lubridate)
# Definition of character strings representing dates
str1 <- "2012-03-15"
str2 <- "30/5/2016"

ymd(str1)

## [1] "2012-03-15"

dmy(str2)

## [1] "2016-05-30"

R 常用技巧

關係式表達 (1)：單一變數

關係式表達 (2) : 向量與矩陣

關係式表達 (3) : and (&) 和 or (|)

關係式表達 (4) : and (&) 和 or (|)

If Structures

If…Else Structures

while loop (1)

while loop (2): 结合if structure

while loop (3): break

for Loops (1)

for Loops (2): 兩層for loop

for Loops (3): break

for Loops (4): 字串處理

計算從 1+2+3+…+100 的值

Question

Answer

Questions: Central limit theorem (C.L.T)

Answers: Code

Answers: n=1

Answers: n=3

Answers: n=50

Functions (1)

Functions (2): 使用函數

Functions (3): 使用函數

Functions (4): Write your own function

Functions (5): Write your own function

Probability Distributions (機率分配)

probability density function

Plot N(0,1)

Plot N(1,3)

Cumulative density function (CDF)

Plot CDF of Normal Distribution

Inverse CDF (quantiles)

Randomly generated numbers (Normal)

Randomly generated numbers (Normal)

Question: Monte Carlo Simulation

Answer

apply 函數家族 (1): lapply()

apply 函數家族 (2): lapply()

apply 函數家族 (3): lapply()

apply 函數家族 (4): sapply()

apply 函數家族 (5)

其它常用技巧(1): 數值函數

其它常用技巧(2): 資料處理函數

其它常用技巧(3): Regular Expressions

其它常用技巧(4): Regular Expressions

其它常用技巧(5): Regular Expressions

其它常用技巧(6): Regular Expressions

Question

Answer

其它常用技巧(7): 日期與時間

其它常用技巧(8): 日期與時間

其它常用技巧(9): 日期與時間