1) The underlying relationship between Y and X is Y_i=βX_i+ε_i, where the density function ofε_i is f(ε_i)= exp(-ε_i) for ε_i non-negative and zero otherwise. The values of X are observed, but Y is an unobserved latent variable. The only thing you know is the value of an indicator variable Z that is 1 when Y is positive and 0 when it is not positive. Using the data below, find the maximum likelihood estimate for β and test the hypothesis that β=5 using a likelihood ratio test.

X	Z
2.330202	1
0.412245	1
-0.95171	0
0.652971	1
1.694773	1
0.11577	1
2.342919	1
2.111553	1
-1.45119	0
-0.41914	0
-1.876	0
1.911599	1
-0.4387	0
1.452094	1
1.928657	1
-2.48699	0
1.704174	1
0.231499	1
-2.403	0
2.293572	1
1.140321	1
-0.69274	0
-1.09291	0
2.016314	1
-0.75442	0
-1.84381	0
-1.6475	0
-2.37047	0
-2.35681	0
-0.14848	0

推倒了半天

觉得应该是找个β maximizing L=∏(1-EXP(βX_i)) for all Xi<0

不知道对不对，而且不知道用什么软件做，老师上课好象说用matlab，我不会，我只会eviews