Assuming a computer is available, plot the pdfs of the random variables defined in parts (a)–(e) below. Obtain an overlay plot of all five pdfs, also. In R the domain values of the pdfs can easily be obtained by using the seq command. For instance, the command x<-seq(-6,6,.1) returns in x a vector of values between −6 and 6 in jumps of 0.1.
(a) X has a standard normal distribution.
(b) X has a t-distribution with 1 degree of freedom.
(c) X has a t-distribution with 3 degrees of freedom.
(d) X has a t-distribution with 10 degrees of freedom.
(e) X has a t-distribution with 30 degrees of freedom.