Shannon Entropy

 

Define Shannon Entropy. Provide an example using a short 10-mer of DNA.

 

Sample Solution

Shannon’s measure of “information entropy” [1, 2] is a key idea in information theory. Shannon’s Entropy metric for information has an intuitive manner of understanding, remembering, and/or recreating it. Information can be thought of as variables that be stored in or conveyed as variables that can take on various values. A variable can be thought of as a storage unit that can take on one of several possible specified values at different times, following some process for taking on those values. Informally, we obtain information from a variable by inspecting its value, much like we obtain information from an email by reading its contents.

direct taxes such as the proposed tax on red meat are highly regressive. This means that families on low incomes will struggle to cope with the increase in the price of red meat as it is these families that have lower disposable incomes due to their inability to save. Therefore these families are paying a higher percentage of their incomes in taxes compared to the rich. One example where this is clearly seen is the excise duty of cigarettes. It is well known that most cigarette smokers are on lower incomes anyway so this tax is highly regressive. Remler 2004 found that due to recent significant rises in cigarette taxes, the issue of regression is now a more substantial issue. To illustrate, in New York City their federal cigarette taxes are now $3.39 per pack. This makes the tax bill over $1200 per annum for a pack-a-day smoker which is highly significant to those on poor incomes (Remler 2004).

To conclude, it is clear that if left to the market there will be market failure where the consumption of red meat is concerned, so the government will need to intervene somehow to correct this. However, it is up to the government to ensure that their government intervention does not need to government failure: where government intervention, in this case, taxation subsequently leads to a misallocation of resources by distorting the price mechanism. To avoid this, it is evident that significant regulation will need to be implemented alongside the taxation despite the expenses, to avoid government failure and ensure maximum efficacy of this possible tax in the long-run.

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