Please assist with part (c) of this problem. In part (a) I determined that f_X,Y(x,y) = 4/33(x²y+2) and in part (b) I determined that

P(x,y in Q1) = 127/352

P(x,y in Q2) = 73/352

P(x,y in Q3) = 67/352

P(x,y in Q4) = 85/352

[1] ln Major League Baseball, an analytical pitching coach established a probability distribution for the probability a certain pitcher would deliver a pitch to a location within the strike zone. The strike zone is the 2D rectangular region in a plane perpendicular to the ground with dimensions 1.5 feet (~ width of the plate) and ~ 2 feet (distance from the knees of the hitter to the uniform letters). We may think of the strike zone as a rectangular region with (X, Y} vertices {0, 0}, {1.5, 0), (1.5, 2), and (D, 2). The pitch will travel in a manner ~ normal to this region and will pass through the strike zone. Consider a hitter in question as left handed and, with respect to the X direction, stands in the negative domain and reaches his bat across the plate in positive X [:1] Consider the probability distribution for a pitch location (X, Y) as following fx_p{x.y) = {7(ny + 2): o s x s 1.5,o s y s 2 Determine the value of C that will make this a valid probability distribution [b] Think of the strike zone as being broken into 4 quadrants with the point (015, l) as the center point and quadrant naming convention 14 following what we do for the unit circle in trigonometry (upper right = l and counter clockwise names increasing to 4). Using your result in [a], compute the probability of a pitch landing in each of the four quadrants (Q); that is, compute P((x, y) E Q), i = 1, 2, 3, 4. Hint: This is a good time to reaffirm your calculation for C in part [a] as we are considering pitches in the strike zone as representing the sample space. [c] This hitter hits safely with a different probability according to the quadrant of the strike zone the pitch is in. We have, P(hit safely IQ) = (0.35, 0.2, 0.45, and 0.3) for quadrants i = 1, 3, 3, 4-, respectively. What is the probability this hitter will hit safely if he hits the next pitch delivered in the strike zone