Looks like the PMF is supposed to be
which is kinda weird, but it's not entirely clear what you meant...
Anyway, assuming the PMF above, for this to be a valid PMF, we need the probabilities of all events to sum to 1:
Next,
If
, then 
, where we take the positive root because we know 
can only take on positive values, namely 1, 2, and 5. Correspondingly, we know that 
can take on the values 
, 
, and 
. At these values of , we would have the same probability as we did for the respective value of . That is,
Part (5) is incomplete, so I'll stop here.
which is kinda weird, but it's not entirely clear what you meant...
Anyway, assuming the PMF above, for this to be a valid PMF, we need the probabilities of all events to sum to 1:
Next,
If
Part (5) is incomplete, so I'll stop here.
