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Ethical AI and Algorithmic Bias: Addressing ethical issues surrounding AI, including fairness, transparency, accountability, and bias in algorithms, is crucial. Ensuring AI systems make unbiased decisions and are used ethically is an open area of research.

You have a data set of 4096 daily observations and would like to estimate the Hurst exponent for that data like we discussed in the lectures. In the first iteration, you want to operate with two data samples consisting of 2048 non-overlapping observations and in the last iteration you want to have 1024 data samples consisting of 4 non-overlapping observations. How many data clusters do you have in total? You perform the following log-log regression: In(R/S)k = In(C) + HIn(k) + u. The estimated Hurst exponent is 0.72. If you implement the following hypothesis test,

Ho: H = 0.50 versus H1: H > 0.50,

what is your dependency structure under the null hypothesis? What is the corresponding reference distribution under the null hypothesis? Assuming that you apply a standard significance level of 5%, what is the critical value? Assume now that you run the test and your

estimated test statistic has a value of ^ = 1.81. What do you conclude concerning the

dependency structure of your data?

Big Data Processing and Analysis: Effectively managing, processing, and analyzing vast amounts of data (big data) in real-time remains a challenge. Developing algorithms and frameworks that can handle large-scale data efficiently and extract meaningful insights is an ongoing pursuit.