The Higher Education Research Institute at UCLA collected data from 203,967 incoming first-time, full-time freshmen from 270 four-year colleges and universities in the U.S. 77% 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 sex-couples should have the right to legal marital status. Let the random variable X = the number that reply "yes", X N B(8,0.77). (a) Construct the probability distribution function (PDF). Round your answers to four decimal places. P (w) Number Number Number Number Number Number Number Number Number (b) On average (u), how many would you expect to answer yes? Round your answer to two decimal places. (0) What is the standard deviation (0')? Round your answer to two decimal places