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Report#

We do not expect long answers; please, 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 the Python code, whenever possible.

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Question 1

What is the expected value and standard deviation of the ice thickness after 5 days (\(\mu_H\) and \(\sigma_H\))? There should be two sets of results.

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?

Question 3

How do we obtain the “true” distribution of \(H_{ice}\), and what does it look like?

Question 4

Are the propagated and simulated \(\mu_H\) and \(\sigma_H\) values equivalent?

Question 5

Is the Normal distribution a reasonable model for \(H_{ice}\)? If yes, justify why?

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.

Question 7

Why is the sampling distribution not the “true” distribution?

Question 8

In Task 3.2, we look at the Cumulative Distribution Function (CDF) for the fitted Normal distribution and sampled distribution. What do you observe? How will you justify the differences between the two results?

Question 9

Lastly, provide the expression for the (1st order only) Taylor approximation of Mean-Variance based on the assumption that the two input random variables are now correlated, i.e. \(\sigma_{12} \neq 0\). Then, answer the following sub-questions:

  1. How does the Mean of ice thickness change?

  2. How does the Standard Deviation of ice thickness change? When does this increase or decrease?

End of file.

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