CEGM1000 MUDE: Week 1.2, Friday, Sep 13, 2024.
This assignment does not need to be turned in.
Most of the questions require you to finish Analysis.ipynb
first, but depending on how you allocate tasks between group members, it is possible to work on this in parallel. Make sure you save time for peer reviewing each others work before completing the assignment!
We don't expect long answers; be as concise as possible (just a few sentences max, usually); however, it is critical to support your arguments with qualitative observations (e.g., describe specific figures) and quantitative evidence (report results of calculations, values, etc) from Analysis.ipynb
whenever possible.
Question 1
What is the expected value and standard deviation of the ice thickness after 3 days ($\mu_H$ and $\sigma_H$)? There should be two sets of results.
Write your answer here.
Question 2
Explain whether we should use the expected value for our prediction, or whether we should also account for the variability of the thickness estimate in the subsequent phases of our analysis?
Write your answer here.
Question 3
How do we obtain the "true" distribution of $H{ice}$, and what does it look like?_
Write your answer here.
Question 4
Are the propagated and simulated $\mu_H$ and $\sigma_H$ equivalent?
Write your answer here.
Question 5
Is the Normal distribution a reasonable model for $H{ice}$?_
Write your answer here.
Question 6
Using the loop in Task 3.1, explore the effect of sample size on the results. Describe the observations you make and explain why they are happening.
Write your answer here.
Question 7
Why is the sampling distribution not the "true" distribution?
Write your answer here.
Question 8
Describe the values of the function of random variables (the output) for which we might expect the model to be inaccurate. Quantify this inaccuracy by comparing the probability calculated with the assumed distribution with the frequency of similar values observed. Use the empty cell in Task 3 in the Analysis.ipynb
file for computations.
Hint: you can count the number of values in an array that conform to a specific boolean condition usingsum(MY_ARRAY <= MY_VALUE)
. It may also be useful to find the length of an array with len(MY_ARRAY)
.
Write your answer here.
Question 9
Test your learning for this week! Do Exercise 2 on the Q1 Exam from 2023, which you can download using this link.
You can write your answer on a separate piece of paper; it is good practice for the exam.
End of file.
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