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.

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.

## This question was asked on Mar 22, 2010.

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