You are asked to determine the most likely value of X or the mode of this poisson distribution.
in which lambda is 2.2
Consider for two cases, if P(X=x+1)>P(X=x), then 2.2>x+1, x<1.2 so x=1
If P(X=x+1)<P(X=x), then 2.2<x+1 , x>1.2 so x=2,3,4,...
Do you see that P(X=2) has the highest probability? That implies that the value of X most likely to occur is 2. Calculate its probability.
(10) Adjust the mean to get 1/12.