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Let x have a uniform density p(x|) U(0, ) = ( 1/, 0 x 0, otherwise. (a) Suppose that n samples D = {x1, . xn} are drawn independently according to...

Let x have a uniform density
p(x|)  U(0, ) =
(
1/, 0  x  
0, otherwise.
(a) Suppose that n samples D = {x1, . . . xn} are drawn independently according to p(x|).
Show that the MLE for  is max[D] - that is, the value of the maximum element in D.
(b) Suppose that n = 5 points are drawn from the distribution and the maximum value of
which happens to be 0.6. Plot the likelihood p(D|) in the range 0    1. Explain
in words why you do not need to know the values of the other 4 points.

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