Solve both problems hand written and show work will give thumbs up

5. In a vehicle assembly line, each vehicle's paint finish is rated on a quality scale of 0 to 8, where 0 is unacceptable and 8 is perfect. Let X = the quality score of a randomly selected vehicle, and the PMF is: X 0 2 3 4 5 6 7 8 p(x) 0.003 0.007 0.010 0.065 0.100 0.200 0.350 0.165 0.100 What is the expected value of X? (5 points) 6. A random variable X has the following PMF X = x -3 -2 0 1 3 P{X = x} 0.2 0.2 0.1 0.2 0.3 (a) If Y=g(X)=[X2-2), calculate the PMF of Y and draw the CDF of Y (10 points) (b) Compute P(2