monete10000 = rbinom(n = 10^6, size = 10000, prob = 0.5)
hist(monete10000, col = "orange")




indirizzo = "http://www.biostatisticaumg.it/dataset/cholesterol.csv"
cholesterol = read.csv(indirizzo, header = TRUE)
attach(cholesterol)
medieHDLchol = numeric(10000)
for (i in 1:10000) {medieHDLchol[i] = mean(sample(HDLchol, size = 100))}
par(mfrow = c(1,2))
hist(HDLchol, col = "violet")
hist(medieHDLchol, col = "orange")



curve(dnorm, from = -3, to = 3)


(dnorm(1) == dnorm(-1)) 
(dnorm(-2.3456) == dnorm(2.3456))


pnorm(-1.23456) 
1 - pnorm(1.23456)


pnorm(-1)
1 - pnorm(1)
pnorm(-1) == 1 - pnorm(1)
pnorm(-2.3456) == 1 - pnorm(2.3456)


pnorm(1) - pnorm(-1)
pnorm(2) - pnorm(-2)
pnorm(3) - pnorm(-3)


qnorm(0.05)
qnorm(0.95)



set.seed(987)
mu = 3500
sigma = 240
mu + sigma * rnorm(n = 4)
set.seed(987)
rnorm(n = 4, mean = mu, sd = sigma)


(3800 - 3500)/240



set.seed(7155)
normali = rnorm(20)
hist(normali, col = "orange")


uno = rnorm(70)
due = exp(uno)
par(mfrow = c(1,2))
qqnorm(uno)
qqline(uno)
qqnorm(due)
qqline(due)







d1 = sample(1:6, size = 10000, replace = TRUE)
d2 = sample(1:6, size = 10000, replace = TRUE)
d3 = sample(1:6, size = 10000, replace = TRUE)
d4 = sample(1:6, size = 10000, replace = TRUE)
d5 = sample(1:6, size = 10000, replace = TRUE)
somma = d1 + d2 + d3 + d4 + d5
prodotto = d1 * d2 * d3 * d4 * d5
par(mfrow = c(1,2))
hist(somma, col = "orange")
hist(prodotto, col = "violet", xlim = c(0, 2000), breaks = seq(0, 8000, 100))





summary(prodotto)







#####   neonati = rnorm(176400, 3500, 420)


piccolo = matrix(neonati, ncol = 4, byrow = TRUE)
mediacampioni4 =  apply(piccolo, MARGIN = 1, FUN = mean)

round(piccolo[1,], 0)
mediacampioni4[1]
round(piccolo[2,], 0)
mediacampioni4[2]



round(mean(mediacampioni4), 0)
round(sd(mediacampioni4), 0)  ## prendere nota





medio = matrix(neonati, ncol = 9, byrow = TRUE)
mediacampioni9 =  apply(medio, MARGIN = 1, FUN = mean)
grande = matrix(neonati, ncol = 16, byrow = TRUE)
mediacampioni16 =  apply(grande, MARGIN = 1, FUN = mean)
enorme = matrix(neonati, ncol = 25, byrow = TRUE)
mediacampioni25 =  apply(enorme, MARGIN = 1, FUN = mean)





par(mfrow = c(2,2))
hist(mediacampioni4, col = "yellow", xlim = c(2500, 4500))
hist(mediacampioni9, col = "gold", xlim = c(2500, 4500))
hist(mediacampioni16, col = "orange", xlim = c(2500, 4500))
hist(mediacampioni25, col = "red", xlim = c(2500, 4500))


boxplot(mediacampioni4, mediacampioni9, mediacampioni16, mediacampioni25, 
        col = c("darkorange1", "darkorange2", "darkorange3", "darkorange4"))