Question 3 For the student t distribution, the lower the degree of freedom, the fatter the tails. This exercise helps you visualize the fact.

1.Using the rt command in R, simulate 10000 observations from a student t distribution with the degree of freedom equal to 5. Do the same thing for t distributions with degrees of freedom equal to 20 and 100 respectively. You end up with three t-distributed samples with different degrees of freedom. Calculate the means and standard deviations of the three samples.

2.To compare the extent of deviation from normality, it is better to first standardize all three samples to have a mean of zero and a standard deviation of one. Use the scale function in R to do it. Make QQ plots of the three standardized samples and arrange them in one plot (Hint: Use par(mfrow=c(1,3)) before you start plotting). Do you find the pattern you expect, that is, the lower the degree of freedom, the fatter the tails?