Probability and Statistics for EngineeringHomework 5Spring 2011(due Tuesday, March 1)(1) Completely simplify the value . (Keep it exact rather than getting a decimal/#$lnapproximation for it.) This should prove to be useful below.(2) Consider the following function , which is a density function for a continuous random0variable .\0ÐBÑ œ /! Ÿ B Ÿ$*%#Bln(a) Find the mean of directly (via integration, using the definition of the mean). Show\all your work, including the details of the integration. Give your answer in exactbothform (in terms of logarithms and/or exponentials, completely simplified) as aanddecimal, rounded to four decimal places.(b) Find the moment generating function for . Show your work. There won't be much\simplifying you can do at the end, and that's OK.(c) Find the mean of using the moment generating function. Show your work.\Hint 1. Of course, your answers for (a) and (c) should match. If they are not the same,don't change something randomly to force them to match.
This is the end of the preview. Sign up
access the rest of the document.