#EXO1

a<-c(3,5,7,11)
a[2]
a[1:3]
a[a>5]

#EXO 2

stat.log <- function (x)
{
  n<-length(x)
  s<-0
  for (i in (1:n)) {s<-s+x[i]}
  s/n
}

stat.log(a)

#EXO 3

#a

echantillon <- rnorm (10,0,1)
echantillon10 <- rnorm (50,0,1)
echantillon11 <- rnorm (500,0,1)
echantillon
#b

echantillon2 <- rexp(10,0.1)
echantillon2

echantillon3 <- rexp(50,0.1)
echantillon3

echantillon4 <- rexp(500,0.1)
echantillon4

#c

echantillon5 <- runif(10,0,1)
echantillon5

echantillon6 <- runif(50,0,1)
echantillon6

echantillon7 <- runif(500,0,1)
echantillon7

#EXO4

produits <- c("Cancoillotte","Saucisse de Montbéliard","Edel de Clairon", "Saucisse de Morteau","Mont D'or","Vin jaune")
chiffres <- c(1950,470,670,920,750,715)

pie (chiffres, labels = produits)

#EXO 5

barplot(chiffres,names = produits)

#EXO 6

enfants <- c("0","1","2","3","4","5","6",">6")
freq <- c(235,183,285,139,88,67,3,0)

pie(freq,labels=enfants)

#EXO 7

#1
echantillon8 <- c(91.6,35.7,251.3,24.3,5.4,67.3,170.9,9.5,118.4,57.1)

echantillon9 <- sort(echantillon8)

#2

hist(echantillon8,prob=F,breaks=seq(3,260,50))

#3

h<-hist(echantillon8,prob=T,breaks=c(3,15,50,90,160,260))
abs<-h$mids
abs
#4


lines(h$mids,h$density)

#EXO 8

h1 <- hist(echantillon,prob=T)
h10 <- hist(echantillon10,prob=T)
h11 <- hist(echantillon11,prob=T)
h2 <- hist(echantillon2,prob=T,breaks=c(1,40,5))
h3 <- hist(echantillon5,prob=T,breaks=c(0.1,1,0.2))

#EXO 9

#1 et 2
x <- summary(a)

moyenne <- mean(x)
variance <- var (x)
mediane <- median(x)
quartile <- quantile (x)

moyenne
variance
mediane
quartile

#3

summary (echantillon2)


# EXO 10

#1

val <- 1
x<-seq(0,10,1)
y<- -4*x+1+ rnorm(length(x),0,val)

plot(x,y)

#3

b0 <- mean(y)-cov(x,y)/var(x)*mean(x)
b1 <- cov(x,y)/var(x)
b0
b1
y1 <- b1*x+b0

plot(x,y1)

#4
reg <- lm(y~x)

summary(reg)


abline(reg)

coeff <- cor(x,y)
coeff

erreurmoyenne <- function (x)
{
  n <- length (x)
  m <- mean(x)
  erreurmoy2 <- 0
  for (i in(1:n)) {s <- (x[i]-m)^2}
  erreurmoy <- 1/n
}

erreurmoyenne(x)

erreurmoy = var(y) - (1-cor(x,y))^2
erreurmoy

#Exo11


lines(density(echantillon11))
plot(ecdf(echantillon11))