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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. 61.3% 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 ~ B (8, 0.613). (a) Construct the probability distribution function (PDF). Round your answers to four decimal places. P (x) 0 Number T Number 2 Number 3 Number 4 Number 5 Number 6 Number 7 Number 8 Number (b) On average (u), how many would you expect to answer yes? u = Number (c) What is the standard deviation (o)? Round your answer to two decimal places. Number