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Least squares estimation (statistics)
I am confused as to how to interpret this question:
Do we have a distribution of a discrete stochastic variable that can take on 3 outcomes 0, 1 and 2 and their probabilities are what is given as P(Xi=a)? Also how is small xi related to big Xi?
Yes, I think your interpretation is correct.
Xi (big) represents the stochastic variable itself while xi (small) is a concrete observation (outcome) of that variable.
So the outcome 1 was observed twice (x1 and x2) and the outcome 2 was observed once (x3)?
Exactly.
