Project Report
1.
Using the PMF obtained from the relative frequency approach, do you think you could
give your boss an answer?
After calculating the relative frequency PMF using the provided data, let check the
probability of having more than 10 users in a one-second interval. We can see that the
probability is significant, it indicates a higher likelihood of exceeding the specified
threshold, so I can inform my boss about the potential issue of dropping users.
Probability of dropping users (Relative Frequency): 0.5
2.
Using the parametric approach, what is your new estimated
𝛼
for the question your boss
asked you?
In the code:
alphaHat = mean(userData);
The code calculates the mean of the userData, and this mean value (alphaHat) is used as
an estimate for the parameter α in the Poisson distribution. This parameter represents the
average rate of user connections.
Alpha is 10.650
3.
The code calculates the Poisson PMF using the estimated α (alphaHat) and determines
the probability of having more than 10 users in a one-second interval. The result is stored
in probabilityMoreThan10Poisson: 0.4977
4.
Using the parametric method has the following advantages:
Simplicity: Compared to the relative frequency approach, the Poisson distribution
simplifies the model by requiring the estimation of a single parameter.
