## ----setup, include=FALSE---------------------------------------------------------------------------------------------------------------------------------------------------------------
knitr::opts_chunk$set(echo = TRUE)


## ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
library("dslabs")
data(murders)
head(murders)
new_names<-ifelse(nchar(murders$stat)>8, murders$abb, murders$state)
new_names


## ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
# Write a function compute_s_n with argument n that for any given n computes the sum of 1 + 2^2 + ...+ n^2
compute_s_n <- function(n){
  x <- 1:n
  sum(x^2)
}
# Report the value of the sum when n=10
compute_s_n(10)


## ----Simulation-------------------------------------------------------------------------------------------------------------------------------------------------------------------------
##simulate 30 samples from N(0,1)
set.seed(313)
sam1=rnorm(30)
##equally split the sample, one as the treatment group and the other 
##as the control group
group<-rep(c("grp1", "grp2"), each=15)
#### Shuffle the group label
sgroup<-sample(group)
group1=sam1[which(sgroup=="grp1")]
group2=sam1[which(sgroup=="grp2")]


## ----pvalue-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------
##perform t.test for the two samples
t.test(group1,group2)



## ----uniform, fig.width=4, fig.height=4-------------------------------------------------------------------------------------------------------------------------------------------------
##generate 1000 samples from uniform distribution 
hist(runif(1000),freq=F,main="Histogram of 1000 random samples from uniform", xlab="Samples")


## ----permutation test, fig.width=4, fig.height=4, fig.align="center"--------------------------------------------------------------------------------------------------------------------
##p-value of 1000 t-tests
getpvalue=function(iteration){
  g1=sample(1:30,15);g2=(1:30)[-g1]
  group1=sam1[g1]; group2=sam1[g2]
  ##perform t.test for the two samples
  return(t.test(group1,group2)$p.value)
}

simpvalue<-sapply(1:1000, getpvalue)

## ----plotp, fig.width=4, fig.height=4, fig.align="center"-------------------------------------------------------------------------------------------------------------------------------
##histogram
hist(simpvalue,xlim=c(0,1),freq = F, main=" Distribution of p values under the null",xlab="p value")


## ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
##(a)
string<-sample(c('A','C','G','T'),10000,replace=TRUE)
##(b)
table(string)
##(c)
ktuple<-function(x, k){
	ans<-NULL
	for (i  in 1:(length(x)-k+1)){
		tmp<-paste(x[i:(i+k-1)], collapse="")
		ans<-c(ans, tmp)
	}
	tab<-table(ans)
	return(tab)
}

ktuple(string, k=3)



## ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
myfactorial<-function(x){
	if (x <0)
		stop("x needs to be an integer > 0")
	if (x==0){
		ans<-1
	} else{
		ans<-1
		for (i in 1:x){
			ans<-ans*i
		}
	}
	return(ans)
}

myfactorial(10)


## ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
myfac2<-function(x){
  	if (x <0)
		stop("x needs to be an integer > 0")
	if (x==0){
		ans<-1
	} else{
	  txt<-paste(1:x, collapse="*")
	  print(paste(txt, "=", sep=""))
		ans<-eval(parse(text=txt))
	}
	return(ans)
}
myfac2(10)