Question

Using R programming language, supply the code for:

Generate a random sample of size 10, 000 from gamma distribution with scale parameter equal to 1 and shape parameter equal to 2, and form it into a 1000 x 10 matrix. Use the apply() function on this matrix to compute the means of the 1000 rows. Note that the resulting vector comprises the mean of 1000 random samples of size 10 from the above distribution. Examine the distribution of the sample mean random variable graphically using the vector of simulated sample means and the R function hist(), plot(), boxplot(), and qqnorm(). As an argument to the plot() function, use the object created by using density() function on the mean vector.

Note: If you execute the R command par(mfrow = c(2, 2)) before you execute any of the plot commands, the 4 plots will appear in a single page.

Answer 1

Answer:

R Code:

x<-rgamma(10000,shape<-2,scale<-1)
dim(x)<-c(1000,10)
mean_xrow<-apply(x,1,mean)
par(mfrow=c(2,2))
hist(mean_xrow)
plot(mean_xrow)
boxplot(mean_xrow)
qqnorm(mean_xrow)
par(mfrow=c(1,1))
plot(density(mean_xrow))

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