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4 A car panel is spray-painted by a machine, and the technicians are particularly interested in the thickness of the resulting paint layer. Suppose that the random variable X measures the thickness of the paint in millimetres (mm) at some randomly chosen point on a randomly chosen car panel. X takes values between 1 and 3 mm with cumulative distribution function r<1 F(x) + 1:5109 (a) What is the probability that the paint thickness at a particular point is less than 1.5 mm? (b) Construct the probability density function of X. (c) Given E(X?) = 4.2, what is the variance of the paint thickness? crv113e

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