Hints and/or comments about Problem 20

• This problem can be done the old-fashioned way, with pencil and paper (or pen and paper for the daredevils amongst you), provided that you use integral tables or do integration by parts correctly. Still, since I think you'll find something like Maple or Mathematica (or I guess anything that can do numerical integration) useful for some of the later problems, you may want to check your answers to this problem using some sort of software (to protect against calculus mistakes and/or to make sure that you know how to use the software properly).
• For part (a), you may want to start by finding (using pencil and paper), the inverse cdf. The inverse cdf can be used to find the median and the percentiles needed for the trimmed mean. (You could check your percentiles using statistical software that will find the inverse cdf values for exponential distributions.)
• The gamma distribution of part (b) is the same shape as a chi-square distribution, differing only in scale. So software that will supply inverse cdf values for chi-square distributions may come in handy for obtaining the median and percentiles that are needed (but you have to multiply the chi-square values by a scale factor to obtain percentiles for the gamma distribution).