PROBLEM Maximum likelihood meets histograms

Let X 1 , X 2 , · · · , X n be n i.i.d data points drawn from a piece-wise
constant probability density function over N equal size bins between
0 and 1 (B 1 , B 2 , · · · , B N ),
where the constants are θ 1 , θ 2 , · · · , θ N .
Using the fact that the total area underneath a probability density function is 1,
.
Find the maximum likelihood estimate of θ j for j ∈ {1, 2, · · · , N }

Sample Solution