Q1. Consider a Geiger counter in a nuclear power plant that measure the number of radiation counts. We observe π readings from the counter and denote them as π₯1, π₯2, β― , π₯π. It is known that the number of radiation counts follows a Poisson distribution with parameter π.
ππ₯π−π
π(π₯; π) = , π₯ = 0,1,2, β―
π₯!
Find the MLE estimate of π based on the observed values π₯1, π₯2, β― , π₯π.
Q2. Consider the following 20 data samples generated from a Poisson distribution:
π₯1 π₯2 π₯3 π₯4 π₯5 π₯6 π₯7 π₯8 π₯9 π₯10 π₯11 π₯12 π₯13 π₯14 π₯15 π₯16 π₯17 π₯18 π₯19 π₯20
3 1 2 1 2 1 0 2 1 0 5 6 3 2 4 4 0 5 5 3
Plot the MLE estimate for the parameter π as a function of the number of samples (i.e., plot the MLE estimate for π when you consider only π₯1, only π₯1 and π₯2, only π₯1, π₯2 and π₯3, and so on till you consider all 20 data points).
