Homework Problem 18, Due Monday March 29.
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Dataset  Dset3B.asc.gz  in the data-directory on the web-page,

http://www.math.umd.edu/~evs/s798c/Data

contains 1000  values   T_j,  j=1,...,1000 simulated from 
the mixture density

    f(t)  =  2p  e^{-2t}  +  (1-p) lambda  e^{-lambda t} , t > 0

where  0 < lambda < 2  and  0 < p < 1  together constitute the 
unknown parameter  theta = (lambda, p).  Find the Maximum 
Likelihood Estimator for  theta   by two distinct methods:

     (i). Steepest-ascent or Quasi-Newton direct maximization of
the likelihood.

    (ii). The EM algorithm.

   For each method display all iterations required, starting with
the initial guess  theta_1 = (1,0.5),  to converge so that at the 
last iteration the log-likelihood  logLik(theta_n)
changes from  logLik(theta_{n-1})  by no more than 1e-3, and also
||theta_n - theta_{n-1}||_2 < 0.003 .