Parameter esitmation with monte carlo

I am just throwing this out there to see if I can get any help. I am tasked to solve 2 questions.

1. I am given a simple estimation equation (y = a), where the measurment has unit variace. I need to determine the accuracy of the parameter estimate as a function of the number of measurments.
2. Then I need to simulate and verify those results with a monte carlo simulation.

I am not sure what my professor is asking here. 1 do I need to use this equation and use randn to generate random numbers to determine my "y"?

Then 2, how do I model that via monte carlo.

I am not sure I am understanding what needs to be done. Anyone have an idea?

[James Tursa]

Did the professor state that the random variables are normal distribution? So in (1) you are simply asked what the variance of the average of some normal random variables are? I.e., are we to assume that you will be averaging a number of measurements to come up with your estimate? If so, then the answer is pretty easy:

https://en.wikipedia.org/wiki/Sum_of_normally_distributed_random_variables

And then in (2) run some Monte Carlo simulations to see if they match your expectations?