Consider the random variable Y to be the time (measured in minutes) to drink a cup of coffee. Assume Y is distributed as a ramp-up distribution with the following probability density function (PDF): f(y) = ( (y 3)/18 3 y 9 0 otherwise (a) 1 pt What is the population mean (y), also known as expected value (E[Y ])? (b) 1 pt Using a line chart, plot the PDF f(y) for 0 y 10. Label the axes. Copyright c 2022 Paul T. Grogan 1 Creative Commons BY-NC 4.0 License (c) 2 pts Either using calculus or geometry, derive an equation for the CDF F(y). (d) 1 pt Using a line chart, plot the CDF F(y) for 0 y 10. Label the axes. (e) 4 pts Using the inverse transform method, develop a continuous process generator for Y and generate n = 1000 samples y1, y2, . . . , y1000. Report the following: (i) Plot a histogram of the samples using appropriately-sized bins (ii) Sample mean (y) (iii) Sample standard deviation (sy) (iv) 95% confidence interval for population mean