Question 1183558
As it stands the table of values do NOT represent a binomial distribution.  

There is a problem with the probabilities for x = 2 and x = 3 -- they should be interchanged.  


But even more damning reason to say that this is not necessarily a binomial experiment 
is the fact that the pmf only by itself alone does NOT define a distribution. 


A distribution is defined by its underlying experiment, and in this case, there is no description of a binomial experiment ever happening.  
A binomial experiment is a series of Bernoulli experiments, where each experiment/trial is characterized by a "yes-no" (1-0) outcome, 
and the probability for the "yes" or the "no" doesn't change in each repetition of the Bernoulli experiment.