Homework 1

Due 2019 September 13

Report instructions

Please upload one PDF file to Gradescope (Entry code: ME62YG).

For this homework you will implement code (on PrairieLearn) to perform statistical analysis of data, which is representative of analyzing simulation output. You specifically should implement functions that compute the mean value, the standard deviation, the auto-correlation time, and the standard error (please see PrairieLearn for details and instructions). For your report you will be asked to discuss a couple of specific problems related to your analysis.

Data set 1

Data set 2

Data set 3

Data set 4

A data set (download here) was sampled from the distribution \[P(x) = b/(|x|^a + c)\] with \(a = 2.2\) and \(c = 1.0\). The constant \(b\) is determined by the normalization.

Central Limit Theorem

Given a population with a mean \(\mu\) and a finite, non-zero variance \(\sigma\), the sampling distribution of the mean approaches a normal distribution with a mean of \(\mu\) and a variance of \(\sigma'\) = \(\sigma/(N-1)\) as \(N\), the sample size, increases.

This is the Central Limit Theorem and implies that the estimated mean approaches a Gaussian distribution as more points are used.

Now suppose you have you have 2 versions \(A\) and \(B\) of a code that you’re debugging. You run each code 6 times to try to determine if they give the same answers. This yields: \[A=\left\{1.12, 1.52, 1.33, 1.09, 1.20, 1.26\right\}\] \[B=\left\{1.44, 1.34, 1.19, 1.13, 1.56, 1.45\right\}\]