Problem 2 The article The Load-Life Relationship for M50 Bearings with Silicon Nitride Ceramic Balls (Lubraica- tion Engr., 1984: 153159) reports the accompanying data on bearing load life (million revs.) for bearings tested at a 6.45 kN load. 47.1 126.0 289.0 68.1 146.6 289.0 68.1 90.8 229.0 240.0 367.0 385.9 103.6 106.0 240.0 278.0 392.0 505.0 115.0 278.0 This data is given in LoadLife . csv. a. Construct a normal QQ plot. Is normality plausible? b. Construct a Weibull QQ plot. Try the following (somewhat crude) method for getting reasonable estimates. i. For fixed (a, b), find the quantile of order p, F* (p; a, b) for Weibull with (shape, scale) = (a, b). This can be found explicitly. ii. Find the sample median and 3rd quartile of the data set. iii. Equate F* (1/2; a, b) = Sample Median F* (3/4; a, b) = Sample 3rd Quartile. iv. Solve for a, b from the two equations in 2 unknowns to get estimates (a, b). You have effectively equated theoretical median and 3rd quantile to the sample versions to solve for the parameters. v. Find the relationship between a Weibull r.v. and an exponential r.v., and try to generate the theoretical quantiles of Weibull using the qexp () function. Make a Weibull QQ plot using (a, b) and add a proper reference line. Does it look worse than the normal QQ plot