probability and distribution questions

Answer to the following questions (APA format not needed):

Please define each of the following terms:sampled population, random sampling, convenient sampling, judgmental sampling, stratified random sampling, consistency in sampling, relative efficiency. Explain why a sample is of probabilistic nature.

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What is it meant by the term â€œparameter of a populationâ€? Explain why a population can be represented by a random variable.

What is a point estimate, and an unbiased point estimate? Explain howthe sample mean can bean unbiased estimate of the population mean.How do you justify that the sample variance is an unbiased estimate of the population variance? What is the sampling requirement in the latter case? Provide a numerical example of estimating the mean, the variance, and the standard deviation.

Please define each of the following terms, discuss applicability and significance of each:sample statistic, standard error, sampling distribution, and central limit theorem. Include hypothetical examples for better clarity.

What is the z statistic and what qualifies a statistic to be z statistic based on the central limit theorem and the basic properties of normal distributions?What are the limitations of the central limit theorem, and how some of these limitations are bypassed?For example, the z statistic as the sampling distribution in estimating a proportion.

What is the sampling distribution in estimating the variance of a population? What are the properties of this distribution?

What is the alternative of z statistic for normally distributed populations whicheliminates some limitations of the central limit theorem?How this sampling distribution is constructed as combination of a z distribution and a chi squared distribution? What are the properties of this distribution?