five values and will compute the entropy of this thing so it isn't like 1/4 1/4 1/4 1/8 1/8 and we can compute the entropy entropy is 2.25 then let's look at another distribution much more peaked beautiful these are three quarters and then 1/16 for everything else compute the entropy its 1.3 so 1.3 2.25 entropy is a lot larger on the left and on the right why is that because if I run an experiment on the random variable on the left and then want to communicate the outcome Q actually there's many possible outcomes that are pretty likely and so