(1) Let X be a discrete random variable with a probability function given by p (x) = c 7 x, for x = 1,. . . , 6, where is a positive real constant. Determine: (a) the value of the constant c. (b) the probability that X is an odd number. (c) the expected value of X. (d) the variance of X.  Total value of the question: 3, 0 points, with 0, 75 points for each item. (2) Let X be a discrete random variable with a distribution function F (x) =    0, for x <0; 1 2 , for 0  x <1; 3 5 , for 1  x <2; 4 5 , for 2  x <3; 9 10, for 3  x <4; 1, for x  4 . Determine: (a) The probability distribution of X; (b) F (2) and F (2); (c) P (0, 5  X  2, 5); (d) P (X = 0 | X is even).  Total value of the question: 3, 0 points, with 0, 75 points for each item. (3) Let X be a continuous random variable with the distribution function F (x) =    0, for x <0; x 2 2 , for 0  x <1>