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1 Bài về nhà tuần 1

library(ggplot2)
library(extraDistr)

1.1 Poisson Distribution

poisson <- rpois(10000, lambda = 1.5)
summary(poisson)

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   0.000   1.000   1.000   1.472   2.000   8.000

var(poisson)

## [1] 1.46274

sd(poisson)

## [1] 1.209438

poisson <- table(poisson)
poisson <- as.data.frame(poisson)
ggplot(poisson, aes(poisson, Freq)) + geom_col(fill = 'red') + geom_point() + geom_line(aes(as.integer(poisson), Freq), color = 'yellow')

1.2 Student Distribution

student <- round(rt(10000, df = 70),0)
summary(student)

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
## -4.0000 -1.0000  0.0000  0.0175  1.0000  4.0000

var(student)

## [1] 1.105704

sd(student)

## [1] 1.051525

student <- table(student)
student <- as.data.frame(student)
ggplot(student, aes(student, Freq)) + geom_col(fill = 'green') + geom_point() + geom_line(aes(as.integer(student), Freq), color = 'red')

1.3 Chi_square Distribution

chisquare <- round(rchisq(10000, df = 10),0)
summary(chisquare)

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   1.000   7.000   9.000   9.928  13.000  39.000

var(chisquare)

## [1] 20.36685

sd(chisquare)

## [1] 4.512965

chisquare <- table(chisquare)
chisquare <- as.data.frame(chisquare)
ggplot(chisquare, aes(chisquare, Freq)) + geom_col(fill = 'purple') + geom_point() + geom_line(aes(as.integer(chisquare), Freq), color = 'yellow')

1.4 Binomial Distribution

binomial <- rbinom(10000, size = 10, prob = 0.2)
summary(binomial)

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   0.000   1.000   2.000   1.996   3.000   7.000

var(binomial)

## [1] 1.554138

sd(binomial)

## [1] 1.246651

binomial <- table(binomial)
binomial <- as.data.frame(binomial)
ggplot(binomial, aes(binomial, Freq)) + geom_col(fill = 'yellow') + geom_point() + geom_line(aes(as.integer(binomial), Freq), color = 'red')

1.5 Normal Distribution

normal <- rnorm(n = 10000, mean = 1, sd = 4)
summary(normal)

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
## -14.145  -1.726   1.017   1.010   3.756  17.335

var(normal)

## [1] 16.27791

sd(normal)

## [1] 4.034589

hist(normal)

1.6 Exponential Distribution

exponential <- rexp(n = 10000, rate = 1)
summary(exponential)

##      Min.   1st Qu.    Median      Mean   3rd Qu.      Max. 
##  0.000246  0.285396  0.701611  1.016285  1.415225 11.092827

var(exponential)

## [1] 1.04669

sd(exponential)

## [1] 1.023079

hist(exponential)

1.7 Uniform Distribution

Uniform <- runif(10000, min = 0, max = 50)
summary(Uniform)

##     Min.  1st Qu.   Median     Mean  3rd Qu.     Max. 
##  0.00477 12.76534 25.03761 25.11008 37.51878 49.99728

var(Uniform)

## [1] 207.382

sd(Uniform)

## [1] 14.40076

hist(Uniform)

1.8 Triangular Distribution

Triangular <- rtriang(10000, a = 2, b = 10, c = 6)
summary(Triangular)

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   2.053   4.858   6.025   6.008   7.163   9.993

var(Triangular)

## [1] 2.629848

sd(Triangular)

## [1] 1.621681

hist(Triangular)