The Higher Education Research Institute at UCLA collected data from 203,967 incoming firsttime, fulltime freshmen from 270 fouryear colleges and universities in the U.S. 63.8% of those students replied that, yes, they believe that same-sex couples should have the right to legal marital status. Suppose that you randomly pick eight first-time, full-time freshmen from the survey. You are interested in the number that believes that same sexcouples should have the right to legal marital status. Let the random variable X : the number that reply "yes", X N B (8, 0.638). (a) Construct the probability distribution function (PDF). Round your answers to four decimal places. P (:13) Number Number Number Number Number Number Number Number Number {13 (b) On average ([4), how many would you expect to answer yes? Round your answer to two decimal places. ,u : Number (c) What is the standard deviation (0')? Round your answer to two decimal places