Question

R2 IS THE QUESTION,THANKS!
R2. Let X ~ N(μ = 10.82). Following upon we be approximating μwe can see should be 100. For now, let the sample size be n = 3, Pick 3 random numbers from X, compute X', and repeat the process a total of 50000 times. Plot a smooth version of the histogram of these 50000 values for X: the plot(density(...)) command in R will be useful. Now find the average of your 50000 values and make a vertical dotted line in R at this number (match the color of your curve). You have just made a rough picture of the density function for X (when n = 3) and identified its (approximate) expected value. Now you should repeat this process for n = 6, n = 10 and n = 50, Plot all four of these curves (use different colors) and vertical lines on the same set of axes choosing limits on the axes so the picture looks nice. Finally, put a dark solid vertical line at 100. You should be able to see the asymptotic unbiasedness in the picture. Your answer is your code and a rough sketch of the plot you have created RT will , which 2

Answer 1

R code:

x1=matrix(0,nrow=50000,ncol=3)
y1=1:50000*0
x2=matrix(0,nrow=50000,ncol=6)
y2=1:50000*0
x3=matrix(0,nrow=50000,ncol=10)
y3=1:50000*0
x4=matrix(0,nrow=50000,ncol=50)
y4=1:50000*0
for(i in 1:50000)
{
x1[i,]=rnorm(3,10,8)
y1[i]=mean(x1[i,])^2
}
for(i in 1:50000)
{
x2[i,]=rnorm(6,10,8)
y2[i]=mean(x2[i,])^2
}
for(i in 1:50000)
{
x3[i,]=rnorm(10,10,8)
y3[i]=mean(x3[i,])^2
}
for(i in 1:50000)
{
x4[i,]=rnorm(50,10,8)
y4[i]=mean(x4[i,])^2
}
plot(density(y1),lwd=1.5,col=1,ylim=c(0,0.018))
lines(density(y2),lwd=1.5,col=2)
lines(density(y3),lwd=1.5,col=3)
lines(density(y4),lwd=1.5,col=4)
abline(v=10^2,lwd=2,col=1)
legend("topright",c("n=3","n=6","n=10","n=50"),lty=1,col=1:4)
text(160,0.018,expression(mu^2==100))