Flip a coin 100 times. Find the expected number of heads, with its uncertainty (the typical fluctuation).
Roll a die 100 times. Find the expected number of times getting a '6', with its uncertainty.
Roll a die 100 times. Find the expected number times not getting a '6', with its uncertainty.
For each of the three cases:
Express the result (best value ± uncertainty) with uncertainty rounded to one significant digit.
Base your calculations, first, on the Binomial distribution.
Repeat the calculation but now based on the Poisson distribution.
Discuss the appropriateness of the Poisson distribution for these three cases. That is...
Does it seem to give a good approximation? Why should this be so?
Even if a good approximation, the Poisson cannot be quite right. Why not?
Hints: The Poisson approximates the binomial for n large and p small but allows infinite successes.
