2. In the Logistic Regression, we often encounter a function like 3 HI) = 1 + 33' An interesting fact is that: this function f (I) is actually a CDF. (a) (1 pt} If a random variable X has CDF F(.."..'-] = HI] = '3: what is its PDF 1+2," 30(5)? 1What are the mean and median of this random variable? (b) (1 pt; ) Write down a procedure to generate X. Namely, nd a procedure to generate random points from the CDF F{:r) = 13;. (c) (1 pt; Q'} Use Monte Carlo Simulation to generate at least 11 = 1i], 000 points from the CDF 17(5) = 11;. Compare the histogram to the density curve 33(1') of the CDF F(..'I:]. Hint: The Cauchy (0, 1} distribution has a PDF {I} 1 1 33(33th 7r 1 + $2 and the double exponential distribution has a PDF A Pdaprifr) = 58"\