In a charpy impact test, the purpose of the notch is to provide a point of fracture at the same point for each material, to make it a fair test.
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It is 15 times the probability of a randomly selected tank being leaky.
There are two equivalent ways of defining a simple random sample from a larger population. One definition is that every member of the population has the same probability of being included in the sample. The second is that, if you generate all possible samples of the given size from the population, then each such sample has the same probability of being selected for use.
A character that is good for separating samples typically exhibits a high degree of variance or discriminative power across different groups or categories. This means the character's values or features should show clear distinctions between the samples being compared, allowing for effective classification. Additionally, robustness against noise and the ability to maintain distinctiveness under various conditions further enhance the character's utility in separation tasks.
A probability sample is one in which each member of the population has the same probability of being included. An alternative and equivalent definition is that it is a sample such that the probability of selecting that particular sample is the same for all samples of that size which could be drawn from the population.
One of the main reasons for doing so is to check that the assumptions of the errors being independent and identically distributed is true. If that is not the case then the simple linear regression is not an appropriate model.