### Numbers and their operations
x <- 5
class(x)
y <- 6
x+y
x-y
x*y
x/y

### Vectors and their operations
v <- c(1,2,3,4)
class(v)
length(v)
u <- c(-2,1,3,2)
u+v
u-v
u*v
u/v
# dot product
u%*%v
# or
t(u)%*%v

# multiplying vectors to obtain a matrix
u%*%t(v)

### Matrices and their operations
A <- matrix(NA,2,3)
for (i in 1:2){
  for(j in 1:3){A[i,j]=2
  }
}
A
# Alternatively, we could also do
A <- matrix(2,2,3)
A


# This is slightly different from what we did in the tutorial, but see if you can understand
B <- matrix(NA,3,2)
for (i in 1:3){
  for(j in 1:2){B[i,j]=i+j
  }
}
B
# Extract a row or a column from a matrix
B[1,]
B[,2]

# Multiply a matrix onto a vector
w <- c(1,2,3)
t(B)%*%w

# Turn a matrix into a data frame
B_df <- as.data.frame(B)
B_df
# Extract a vector of variables from a data frame
B_df$V2

### Median, Mean, Variance
# Recall the intuition why we need to consider mean together with variance
a <- c(1,2,4,3,7,5,9,11,15,17,19,13,13,12,16,9,14,13,16,2)
# Order a in ascending order
sort(a)
median(a)
mean(a)
var(a)

### Boxplot
boxplot(a)

### Histogram
hist(a)
# Generate randome numbers from a distribution
# you are not required to know the beta distribution, focus on understanding the histogram
b <- rbeta(10000,2,5)
hist(b)
boxplot(b)