By Mark Jerrum
Textual content constituted of notes originating in a postgraduate lecture sequence given through the writer on the ETH in Zurich within the Spring of 2000. Covers the counting of combinatorial buildings and comparable themes, seen from a computational viewpoint. Softcover.
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Extra resources for Counting, sampling and integrating: algorithms and complexity
Definition A simple random sample of size n is a sample that has been selected from a population in such a way that each possible sample of size n has an equally likely chance of being selected. EXAMPLE 1-1 Current Measurements An electrical engineer measures the current flowing through a simple circuit several times and observes that the current measurements are different each time. Can we view these measurements as a simple random sample? What is the population? Solution. If the circuit is the same each time the measurement is made, and if the characteristics of the ammeter are unchanged, then we can view the current measurements as a simple random sample.
2. 3. 4. Using historical data always involves the risk that, for whatever reason, some of the important data were not collected or were lost or were inaccurately transcribed or recorded. Consequently, historical data often suffer from problems with data quality. These errors also make historical data prone to outliers. Just because data are convenient to collect does not mean that these data are useful. Often, data that are not considered essential for routine process monitoring and that are not convenient to collect have a significant impact on the process.
Only if you are very sure that these consecutive readings are taken under identical and unchanging conditions and are unlikely to differ from future observations on the process would it be reasonable to think of these data as a random sample. We have observed 24 consecutive readings and it is very possible that these concentration readings may be different from future readings because chemical processes (and other processes as well) often tend to “drift” over time and may operate differently in different time periods due to changes in raw material sources, environmental factors, or operating conditions that the engineers make as they learn more through experience about how best to run the process.