What’s simple random sampling? Is it possible to sample data instances using a distribution different from the uniform distribution? If so, give an example of a probability distribution of the data instances that is different from uniform (i.e., equal probability). Purchase the answer to view it

**Answer**

Simple random sampling is a popular and widely-used method of sampling in statistics. It involves selecting a subset of individuals from a larger population in such a way that each individual has an equal probability of being included in the sample. This method ensures that the sample is representative of the population and reduces the likelihood of bias.

To perform simple random sampling, each individual in the population should have an equal chance of being selected. This can be achieved by using random number generators, lottery methods, or relying on a systematic selection process. The basic idea is that every individual in the population has an equal and independent chance of being chosen.

There are cases when it might be preferable to sample data instances using a distribution that is different from the uniform distribution. In such cases, the method used is known as stratified random sampling or cluster sampling. These methods involve dividing the population into subgroups or clusters and then randomly sampling from each subgroup or cluster.

For example, let’s imagine a scenario where we want to study the average income levels of individuals in a city. Rather than selecting individuals uniformly at random from the entire population, we could stratify the population into different income brackets (such as low income, medium income, and high income) and then randomly sample from each income bracket. This would ensure that the sample includes individuals from different income groups in proportion to their representation in the population.

Another example is quota sampling, where the population is divided into categories and a fixed number of individuals is selected from each category. This approach aims to ensure that the sample reflects the characteristics of the overall population, even though the selection process may not be entirely random.

In summary, simple random sampling is a valuable and commonly used method for sampling data instances. However, there are situations where it may be more appropriate to use alternative methods such as stratified random sampling or quota sampling, which allow for a distribution of data instances that is different from the uniform distribution.

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