Exercise 2. 1. Let S := exp(X) where X is a normal distribution with parameters ,u and 02. Prove that S has the following density function 1 _ (may? f[s) = e 202 , if s > 0 and 0 otherwise. \\/ 27:50 2. Compute [E[S] . 3. We have a sample of the size of concrete particles in micrometer 3.1;5.0;8.9; 16.0;25.6; 39.1; 109.2. Give an estimator of u if we assume that the size of a particule concrete follows the distribution of S with a x parameter a = 0.7