# Q1.1 We can use as a Calculator

3 + 4*9

4*log(sqrt(5))/sin(2.5*pi) - exp(-3^2)


# Q1.2 We can use R to construct functions and manipulate them
dat <- c(5, 1, 2, 13, 5, 8, 3, 1, 34, 21)	# We create this data using the combine command c().
dat
sum(dat)					# sum of data
length(dat)					# length of data
mean(dat)					# mean of data
sd(dat)						# SD of data
dat - mean(dat)					# Transform data: De-mean data


# Q1.3 We define new variables, by manipulating the data
m_dat <- mean(dat)
sd_dat <- sd(dat)
z_dat <- (dat - m_dat)/sd_dat	 		# We standardized dat
z_dat
dat_m_2 <- (dat - mean(dat))^2			# We square the deviations from mean
n_dat <-length(dat)
var_dat <- sum(dat_m_2)/(n_dat-1)
var_dat


# Q1.4 We can write functions in R
var_f <- function(dat_f) {		
m_dat_f <-mean(dat_f)
	return(sum((dat_f-m_dat_f)^2)/(length(dat_f)- 1))
}

var_f(dat)
sqrt(var_f)


# Q1.5  Quick Summary of Distribution and Sorting
summary(dat)
sort(dat)



# Q1.6 In general, we will read the data from a data file. But, we can create in different ways:
dat_1 <- rep(6,10)			
dat_2 <- seq(from=1, to=25, by=5)	
dat_3 <- runif(10)			# Generate 10 random values from a Uniform(0,1)
dat_4 <- rnorm(10, mean=2, sd=2)	# Generate 10 random values from a Normal(2,4)  
dat_5 <- c(dat_1, dat_2, dat_3, dat_4)	# Combine all the data together


# Q1.7 We create a matrix, using rbind() ("row bind") or cbind() ("column bind"):
A <- rbind(dat_1,dat_3, dat_4)		# 3 rows, 10 columns
A
B <- cbind(dat_1,dat_4, dat_4)		# 10 rows, 3 columns
B


# Q1.8 Graphs
plot(dat, type="l", main="Plot of Data")	# All the data consecutively, only interesting if a time series

dat_prop <- dat/n_dat				# Data as a proportion of size
hist_d <- hist(dat_prop, breaks=6, main="Histogram with breaks", xlab="Generated Data")
lines(density(dat_prop), col='red') 		# lines makes a curve, default bandwidth