A professor examined the performance of their students in a math subject, and a simplified version of the model they fit to the scores is tabulated below. Score (value of X) 45 55 65 75 85 95 probability 0.23 0.20 0.17 0.17 0.16 0.07 (a) Compute E (X) and E (X) using the formula on lecture slide 143. (b) Write down the cumulative distribution function Fx of X. (c) Compute E (X) using the formula on lecture slide 158. (d) In a two-dimensional Cartesian coordinate system, plot the lines 1) y 1; 2) y = Fx (x); 3) x = 0; and 4) x = 95; shade the region surrounded by the four lines and calculate the area of the shaded region.