1. Let xi ~ t(v), i= 1,.,n be n independent random variables, each distributed as a t- distributed random variable with v degrees of freedom. Assume that your data are as follows, and use the line of code below to read the data into R: x=c(2.58,0.31,4.16,-1.96, -0. 19, 7.30, -0.58, 1.59, -0.86, 1.36, -0.60, 0.50, -1.17, -1.14, - 1.90, 0.18, -1.58, -0.16, -0.02, 0.20) a. Look up the pdf for a t-distributed random variable on wikipedia. Write the pdf down, and explain why it might be challenging to analytically find an analytic MLE for v. b. Use "optim" to find the MLE for v given this data. Show all code and clearly give your estimate. The pdf of a t-distributed random variable is given in R by the command "dt"