We will write X - when the sample mean is thought of as a random variable, and write x - for the values that it takes. The sample mean x - is a random variable: it varies from sample to sample in a way that cannot be predicted with certainty. We will likely get a different value of x - each time. Imagine however that we take sample after sample, all of the same size n, and compute the sample mean x - of each one. In actual practice we would typically take just one sample. Suppose we wish to estimate the mean μ of a population. To understand the meaning of the formulas for the mean and standard deviation of the sample mean.To become familiar with the concept of the probability distribution of the sample mean.
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