Problem 5 it is beneved that the duration or heat treatment A and the depth or hardening Y for a specic lot of gears are jointly normally distributed with uX = 20 seconds, m = 0.3 inch, ox = 4.5, 0y = 0.05, and p = 0.87. (a) Compute the regression function Mac) = 1E(Y|X = w). (b) Find the conditional distribution of the depth of hardening given the duration of the treatment is observed to be 18 seconds. (0) Given X = 15, What is the probability that the depth of hardening will be between 0.25 and 0.35