For an 8-bin histogram containing the following number of events {4,6,10,30,30,10,6,4} in order, determine the entropy and the variance.  Then, what is the maximum entropy and the maximum variance for the 8-bin histogram if the 100 events can be distributed in any possible way to the bins?        

Pi
EntropyMeanVariance40.04-4.64385620.18575425N/A0.0160.06-4.05889370.24353362N/A0.135100.1-3.32192810.33219281N/A3.025300.3-1.73696560.52108968N/A195.075300.3-1.73696560.52108968N/A195.075100.1-3.32192810.33219281N/A3.02560.06-4.05889370.24353362N/A0.13540.04-4.64385620.18575425N/A0.01
1
2.565140714.5396.49