'1 EX'
''
'a)'
A <- c(10, 20, 30, 40, 50)
B <- c(5, 10, 15, 20, 25)
A
B
''
'b)'
''
A+B
A-B
A*B
A/B
sum(A)
mean(A)
median(A)
max(A)
min(A)
'c)'
''
seq_1_20 <- seq(from = 1, to = 20)
seq_1_20
seq_even <- seq(from = 2, to = 20, by = 2)
seq_even
seq_step5 <- seq(from = 10, to = 50, by = 5)
seq_step5
'2 EX'
''
'a)'
A <- matrix(1:9, nrow = 3, ncol = 3, byrow = TRUE)
B <- matrix(9:1, nrow = 3, ncol = 3, byrow = TRUE)
A
B
''
'b)'
A + B      
A - B       
A * B     
A %*% B     
t(A)   
''
'ESERCIZIO 3'
'a'
set.seed(123)

# 1. 10 numeri casuali tra 0 e 1
rand_unif <- runif(10, min = 0, max = 1)
rand_unif

# 2. 100 osservazioni da Normale(mean = 50, sd = 10)
rand_norm <- rnorm(100, mean = 50, sd = 10)

mean(rand_norm)
sd(rand_norm)
min(rand_norm)
max(rand_norm)
median(rand_norm)

'b'
rolls <- sample(1:6, size = 1000, replace = TRUE)
freq_abs <- table(rolls)
freq_abs

freq_pct <- round(prop.table(freq_abs) * 100, 2)
freq_pct

'ESERCIZIO 4'
x <- 1:10
y <- c(12, 15, 14, 18, 20, 19, 23, 25, 24, 28)

plot(x, y,
     main = "Scatter Plot di x contro y",
     xlab = "Variabile x",
     ylab = "Variabile y",
     col = 1:10,
     pch = 1:10,
     cex = 1.3)

'b'

plot(y,
     type = "l",
     main = "Serie storica simulata (vettore y)",
     xlab = "Tempo (t)",
     ylab = "Valore di y",
     col = "darkblue",
     lwd = 2)

'c'
hist(rand_norm,
     main = "Istogramma delle 100 osservazioni Normali N(50, 10)",
     xlab = "Valori osservati",
     ylab = "Frequenza assoluta",
     col = "lightblue",
     border = "white")

'd'
A <- rnorm(100, mean = 50, sd = 5)
B <- rnorm(100, mean = 60, sd = 10)
C <- rnorm(100, mean = 70, sd = 15)

boxplot(A, B, C,
        names = c("A (mean=50, sd=5)", "B (mean=60, sd=10)", "C (mean=70, sd=15)"),
        main = "Confronto tra le distribuzioni A, B e C",
        xlab = "Gruppi",
        ylab = "Valori",
        col = c("skyblue", "lightgreen", "salmon"))