setwd("C:/Users/shouhermione/Documents/TA/Nanjing/Karen")
osteo=read.csv('osteo.csv')

#show the variable names
names(osteo)

####1 
#a boxplot of age
#do by hand
median(osteo$Age)

boxplot(osteo$Age,main='Boxplot of age')
#b mean,sd,leaf plot
case=osteo[which(osteo$Osteo==1),]$DPA
control=osteo[which(osteo$Osteo==0),]$DPA

c(mean(case),mean(control))
c(sd(case),sd(control))
stem(case)
stem(control)

#Qc. median/interquartile range for the each osteo group
c(median(case),median(control))
#IQR
c(sum(c(-1,1)*summary(case)[c(2,5)]),sum(c(-1,1)*summary(control)[c(2,5)]))
#boxplot by group
boxplot(osteo$DPA~osteo$Osteo,main='Boxplot of DPA by osteo group')

###2 assign X
#a. 
X=(osteo$DPA<=0.8)+(osteo$DPA<=0.9)+(osteo$DPA<=0.95)+(osteo$DPA<=1)
X=5-X

#density of X, round to the 3rd decimal place 
p=round(table(X)/length(X),digit=3)

#cdf of X
#compute the cumulative probability
Fn<-ecdf(X)
#cumulative probability
pcdf<-summary.stepfun(Fn)[2:6]
plot(Fn,main='ECDF of X')

#mean of X
mean(X)


##########Question 3
#sketch f_X and F_X
f_X<-function(x){
  y=0
  if((x<=8)&(x>=0)) y=0.025*x 
  if(((x>=8)&(x<=10))) y=0.200-.100*(x-8)
  y
}

sample_x=seq(from=-1,to=12,by=1)
sample_y=unlist(sapply(sample_x,f_X))
#sketch f_X
plot(sample_x,sample_y,type='l',xlab='X',ylab='density of X')
#sketch F_X