Q2. The discrete random variable D has the following probability distribution 10 20 30 40 50 k k k k P(D= d) 10 20 30 40 50 where k is a constant. 600 (a) Show that the value of k is 137 121 The random variables D, and D2 are independent and each have the same distribution as D. (b) Find P (D1 + D2 = 80) Give your answer to 3 significant figures. A single observation of D is made. The value obtained, d, is the common difference of an arithmetic sequence. The first 4 terms of this arithmetic sequence are the angles, measured in degrees, of quadrilateral Q (c) Find the exact probability that the smallest angle of Q is more than 50 5