Занятие 2

Кривые

curve(x**2,-3,3)

curve(sin(x),-pi,pi)

Квантили для случайных величин

curve(dnorm(x),-3,3)

curve(pnorm(x),-3,3)

curve(qnorm(x),0,1)

curve(pnorm(x),-3,3,ylim=c(-3,3),asp=1)
curve(qnorm(x),0,1,add = TRUE)
curve(x+0,-2,2,add=TRUE)

Свойства выборок

s <- rnorm(11)
print(s)

##  [1]  0.61360904  0.46532513 -0.85686944  1.25238082  0.34773273
##  [6]  0.04321921  1.46436502  0.58102170  0.92798084  0.04671932
## [11] -0.12004862

print(sort(s))

##  [1] -0.85686944 -0.12004862  0.04321921  0.04671932  0.34773273
##  [6]  0.46532513  0.58102170  0.61360904  0.92798084  1.25238082
## [11]  1.46436502

print(length(s))

## [1] 11

print(summary(s))

##     Min.  1st Qu.   Median     Mean  3rd Qu.     Max. 
## -0.85690  0.04497  0.46530  0.43320  0.77080  1.46400

print(median(s))

## [1] 0.4653251

print(mean(s))

## [1] 0.4332214

print(var(s))

## [1] 0.4313717

print(sd(s))

## [1] 0.656789

print(sqrt(var(s)))

## [1] 0.656789

Гистограммы

hist(s)

hist(s,breaks=10)

hist(s,breaks=100)

s <- rnorm(100)
hist(s)
hist(s,breaks=10)

hist(s,breaks=100)

s <- rnorm(1000)

hist(s)
hist(s,breaks=10)

hist(s,breaks=100)

Эмпирическая функция распределения

s <- 1:10
F <- ecdf(s)
plot(F)

s <- rnorm(10)
F <- ecdf(s)
plot(F)

s <- rnorm(100)
F <- ecdf(s)
plot(F)