# 程序代做 ################################################### – cscodehelp代写

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# Computer Lab 4 – F71SM
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## In the tasks below, fill in any missing code as
## required.
## Make sure you use the help menus in R (e.g.”?mean”
## will open up a help window for “mean()”).
## In some cases, the numerical answers you will find
## may be slightly different from those in the tutorial
## answers, due to rounding in intermediate steps.

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# Sampling distn for X.bar – Normal population

# Generate 500 samples of size n=30 from N(10,4) population
# For each sample compute the sample mean
# Plot a histogram of the sample means
# Compute the mean and variance of the sampling distribution
# and compare them with their theoretical values

nsim = 500 # No. of simulated samples
n = 30 # Sample size
xbar.30 = numeric(nsim) # Initialise vector
for (i in 1:nsim){
x = rnorm(n,10,2)
xbar.30[i] = mean(x)
hist(xbar.30,xlim=c(5,15),freq=F)
# freq=F used to produce bars with proportional areas
# this will be useful later
mean(xbar.30); var(xbar.30)

# Repeat code above (incuding for loop) to see the randomness
# in the sampling distribution

# Repeat the exercise in part (i) for sample size n=100

nsim = 500 # No. of simulated samples
n = 100 # Sample size
xbar.100 = numeric(nsim) # Initialise vector
for (i in 1:nsim){
x = rnorm(n,10,2)
xbar.100[i] = mean(x)
hist(xbar.100,xlim=c(5,15),freq=F)
mean(xbar.100); var(xbar.100)

# Add the theoretical pdf of the distribution of Xbar on the histogram
# Remember, this should be a N(10, 4/100) distribution

hist(xbar.100,xlim=c(5,15),freq=F,main=””) # Draw histogram again
title(main=”Histogram of Xbar and pdf of N(10,0.04)”)
x.grid = seq(9,11,length=200) # Grid of values on ax axis
lines(x.grid,dnorm(x.grid,10,sqrt(0.04)),col=”red”,lwd=2) # Draw pdf

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# Sampling distn for X.bar – Chi-squared population

# Repeat part (ii) from Task 1, by generating 500 samples
# of size n=100 from Chi.Squared(4) population

nsim = 500 # No. of simulated samples
n = 100 # Sample size
xbar.100 = numeric(nsim) # Initialise vector
for (i in 1:nsim){
x = rchisq(n,4)
xbar.100[i] = mean(x)
hist(xbar.100,xlim=c(2,8),freq=F)
mean(xbar.100); var(xbar.100)

# Repeat part (iii) from Task 1
# What is the distribution of Xbar now?

hist(xbar.100,xlim=c(2,8),freq=F,main=””) # Draw histogram again
title(main=”Histogram of Xbar and pdf of N(4,8/100)”)
x.grid = seq(2.5,5.5,length=200) # Grid of values on x axis
lines(x.grid,dnorm(x.grid,4,sqrt(8/100)),col=”red”,lwd=2) # Draw pdf