Homework #2   January 17, 2017     [60 pts]

Please staple your homework pages in the upper left corner.

Due:  (a)  in class Tuesday January 24
      (b)  in mailbox of TA Daniel Cross by close of business 1/25 (Wednesday)


1.  6.26, parts b,c,d   [15 pts]

2.  Suppose X_1,...,X_n is a random sample of failure times from an exponential
    density (with parameter lambda), i.e. lam exp(-x * lam).     [20 pts]

  a) Find the MoM estimate of lambda based upon the first (sample) moment.
  b) Same as (a) but based upon the second moment.
  c) Combine (a) and (b) to get an estimate based upon the first 2 moments.
  d) Find the MoM estimate of Prob(X_1>1), i.e. the first unit fails after
      one unit of time.

3.  7.4   [10 pts]

4.  7.6   [15 pts]
          Notes:  In (b), prove a maximum.  In (c), "if it exists".