Problem 15. Let X denote the vibratory stress of a turbine blade under specified conditions. Suppose the probability density function of X is (x x² f(x; 0) = √½e 20, X ≥0 otherwise 10.23, X3 where > 0. A random sample of ten observations yields x1 = 16.88, x2 = 4.59, x4 = 6.66, x5 = 13.68, x6 = 14.23, x7 = 19.87, x8 = 9.40, x9= 6.51, x10 = 10.95. a. Use the method of moments to obtain an estimate of 0 from a random sample of size n, say, X1, X2, . Xn and compute the value of the estimate for the given data 00 ... x² (you can use So e 2 dx = 原 b. Obtain the maximum likelihood estimate of 0 from a random sample of size n, say, X1, X2, Xn and compute the value of the estimate for the given data. ....