Question

Questions 5-9 will be based on the following code: #Creating a random draw of 1000 numbers u <- runif(1000)

Answer 1

• True
• Student statement is true we can check it by running following R-code

a<-runif(1)
plot(c(1,1),c(min(a),max(a)),ylim=c(0,1),xlim=c(0,1000),col=c("blue","red"))
for(i in 2:1000){
a<-runif(i)   
points(c(i,i),c(min(a),max(a)),col=c("blue","red"))}

• Now the result we got by running the code is following

c(min(a), max(a)) 0.0 0.2 0.4 0.6 0.8 1.0 0 200 400 C(1, 1) 600 800 1000

We have plotted minimum by blue and maximum by red and we can see there is increase in maximum as number of sample increases and tending to one so it is monotone , similarly we can see as the number of sample increasing minimum value is decreasing