Question

Use R to solve this

Thank for your help

3· [Additional problem only for graduate students. Undergraduate students will receive 2 extra credits if solving the additional problems correctly.l (5 points) For each of p 50, 100, 500, 1000, randomly drawn 10000 pairs of indepen dent points uniform in the cube in p-space, [0, 1]P. Then for each pair of two points calculate the distance. Use the n distances to calculate the ratio 25th percentile of the distances 75th percentile of the distances Simulate the process for s = 1000 times to obtain ri, r2: ,r, and make 95% confidence limit of the ratio's for each p. Draw a plot to show the pattern of the 95% confidence limits when P increases and explain. Note that 95% confidence limit is the interval of (2.5th percentile, 97.5th percentile)

Answer 1

##R code

Upper_quantile=numeric(4)
lower_quantile=numeric(4)
p=c(50,100,500,1000)
for(k in 1:4){
r=numeric(1000)
for(s in 1:1000){
dist=numeric(10000)
for(i in 1:10000){
x=runif(p[k])
y=runif(p[k])
dist[j]=(sum((x-y)^2))^(1/2)
}
r[s]=quantile(dist,prob=0.25)/quantile(dist,prob=0.75)
  
}
Upper_quantile[k]=quantile(r,prob=0.025)
lower_quantile[k]=quantile(r,prob=0.975)
}

plot(p,Upper_quantile,type="l",col="red",ylab="Upper and lower quantile")
lines(p,lower_quantile,col="blue")