5. These problems have to do with the lognormal distribution. (a) The normal distribution satisfies 21e22(x)2dx=1 Find the form of the integral after the substitution x=ln(s). This defines the PDF, f(s), for the lognormal distribution where the limits of integration determine the allowed values of s. (b) If f(s) is the PDF found in the above problem, find where f(s) has a maximum value. What happens to the location of this maximum value as 0 ? As ? (c) From the information of the above two problems, and your knowledge of the shape of the normal distribution, give a rough sketch of the lognormal distribution for =0.1 and =2. Do the same for =2 and =2