Question: Problem 3 (12 points in total, 2 points each) Difficulty level: medium Two fair coins are tossed. Let the random variable X denote the total

Problem 3 (12 points in total, 2 points each) Difficulty level: medium Two fair coins are tossed. Let the random variable X denote the total number of heads. (a) What are the possible values, xi of the random variable X? (b) Find the PDF of X, fx (x) and graph it. Also, verify that Zify (xi) = 1. (c) Find the CDF of X, Fy (x), for x=0, 1, 2. (d) Find Fx (-5), Fx (1.3) and Fx (2.7). (e) Find P(1.31.5). (f) Graph the CDF of X. Also, write down the CDF analytically (i.e. write down the formula giving the value of the CDF for every interval on the real line)

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