Problem 2 Two components needed in automotive manufacturing each can be represented in 1 of 3 grades. Let X be the cost of the first component (in hundreds of dollars) and let y be the cost of the second component (also in hundreds of dollars). The following table represents the weekly fraction of cars that utilize each combination of these components. a) What is Cov(X, Y)? Round your answer to three decimal places. :cov.xy = NA y=7_y=9 y=10 x=7 0.05 0.05 0.10 x=9 0.05 0.10 0.35 x=10 0 0.20 0.10 # your code here b) Suppose the random variables measure the cost of each part in dollars, rather than hundreds of dollars. In this case, the random variables would be U = 100X and V = 100Y. What is Cov(U, V)? (This question shows us how changing the units of the random variable can change the value of the covariance) ]:cov.uv = 1350 #your code here ]: # Hidden Test Cell c) What is the correlation coefficient px,y? Save this value as rho.xy . What is the correlation coefficient pu,v? Save this value as rho.uv? Round your answers to three decimal places. ]: rho.xy = NA rho.uv = NA # your cada horo